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If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

Piecewise Functions

I greet you this day,

First: read the story. I tell stories too 🙂
Second: read the notes.
Third: view the videos.
Fourth: solve the questions/solved examples.
Fifth: check your solutions with my thoroughly-explained solutions.
You may use the calculators to verify your answers.
You are encouraged to solve the questions first, before you check your answers.
I wrote the codes for the calculators using JavaScript, a client-side scripting language. I used the AJAX Javascript library for the rest of the codes. Please use the latest Internet browsers. The calculators should work.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
Thank you for visiting.

Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

Story

The event will hold in three days.
Well-cooked and delicious: rice and beans
Options of fish, chicken, cabeza
Dad: Let's not worry about vegan. Those folks would really be hungry.
They need to eat well.
Son: Does it mean that those who are vegan do not eat well?
Dad: I did not say that. Do not force words into my mouth.
Son: I just asked a question, Dad.
What about al pastor?
Dad: No, we do not eat pork.
Why should we give people what we do not eat?
Okay, let's go and order these burritos.

Dad: Buenas tardes, señora
How are you doing today?
Son: Good afternoon, Mama Esther.
Esther: Good afternoon. I am doing well.
How are you doing too?
Dad: We are doing well.
Thank you.
How much are your burritos?
Esther: It's $\$7.00$each. Guacamole costs extra ¢$50$each. Dad: We want to place an order for$1000$burritos. Son: Well-cooked: rice and beans; fresh avocados...everything No guacamole. Esther: Okay... Dad:$300$pescado;$300$cabeza;$400$chicken How much is the cost? Esther: How soon do you need them? Dad: In three days. Esther: Would I deliver them, or would you pick them up? Dad: We shall pick them up. Esther: It's going to be$\$7$ each for the first $300$ burritos
$\$6$each for the next$300$, and$\$5.00$ each for the remaining $400$.
Fair enough?
So, the price is ...
$\$2100$for the first$300$+$\$1800$ for the next $300$ + $\$2000$for the remaining$400$Total of$5900$Add$10\%$tax of$5900$That gives$\$590$
Total cost of $\$6490.00$Son: Dad, I could calculate the cost another way. Dad: What way? Is it better than the way Esther did? Son: For many orders, yes! And for writing a computer program to calculate it. Dad: Interesting. What is it? Son: We learned it in school. Mama Esther did it as a simple Arithmetic. Mr. C called it the Manual method. Then, he taught us to do it algebraically ... using the Piecewise Function method. I think it is much better. Dad: Okay, what's the method? Son: We begin by defining the variables involved. Let$b$= buritto and$c$= cost Which variable depends on the other variable? Son: Does the buritto depend on the cost, or does the cost depend on the number of burritos? Dad: The cost depends on the number of burritos. Son: That is correct. We write it this way:$c = f(b)$It can also be written as:$c(b)$Dad: Okay... Son: So,$c(b)$= $$c(b) = \begin{cases} 7b; & \quad 1 \leq b \leq 300 \\[3ex] 6b + 300; & \quad 300 \lt b \leq 600 \\[3ex] 5b + 900; & \quad 600 \lt b \leq 1000 \end{cases}$$ Dad: How is this better than the way Esther did it? Son: Say you wanted to order$900$burritos How much would it cost excluding the taxes? Dad:$\$7$ for the first $300$ gives $\$2100\$6$ for the next $300$ gives $\$1800\$5$ for the remaining $300$ gives $\$1500$That gives a total of$\$5400$
Son: How many steps did you do before you got the answer?
Son: I shall do only two steps before I get that answer.
$c(900) = 5(900) + 900 = 4500 + 900 = 5400$
Dad: You used the $3rd$ equation because $900$ falls in ...
Son: that piece...yes...in that domain.
Dad: That is interesting! How did you get those equations?
Son: Welcome to Piecewise Functions!, Dad.

Overview of Piecewise Functions

Objectives

Students will:
(1.) Define piecewise functions.
(2.) Discuss piecewise functions.
(3.) Discuss real-world applications of piecewise-functions.
(4.) Give examples of mathematical functions that are piecewise functions.
(5.) Graph piecewise functions.
(6.) Analyze the graphs of piecewise functions.
(7.) Solve problems involving the application of piecewise functions.

Skills Measured/Acquired

(1.) Use of prior knowledge
(2.) Critical Thinking
(3.) Interdisciplinary connections/applications
(4.) Technology
(5.) Active participation through direct questioning
(6.) Research

Homework Assignment

Students should research real-world applications of piecewise functions.

(1.) Write the word problem (real-world application).
(2.) Solve solve questions (numbers) "manually" for each piece/interval.
(3.) Write the piecewise function for the word problem.
(4.) Solve those questions again using the piecewise function.
(5.) Check to ensure that you get the same answers (verify your answers) using both methods (manually and piecewise function).
(6.) Write a computer program that solves that word problem.
(7.) Verify your answers again with the computer program.

Check for prior knowledge. Ask students about these terms.

Vocabulary Words

Bring it to English: piece, step, hybrid, exception, except, condition
Bring it to Math: piecewise, function, piecewise-defined, hybrid, domain, range, intercepts, x-intercept, y-intercept, graph, continuity, discontinuity
Bring it to Computer Science: conditional statements, if, if-else, if-elif

Why Study Piecewise Functions?

Ask students to give examples of scenarios where exceptions have been made, or where certain conditions have been used. Let us begin with a simple example.

At some Golden Corral restaurants in the U.S, children aged 3 years and under (at most 3 years) eat free.
Let us analyze the Kid's Buffet. The information is found here.

                        It is also written here for you:
Ages 3 and under:                   Free
Ages 4 - 8:                         $5.99 Ages 9 - 12:$6.99


As you see, there are different prices (costs) for children in a certain age group.
So, you only eat free if you are at most $3$ years old. That is a condition that must be satisfied before you eat free.
When writing a computer program for this function, you have to use conditional statements.

Let us write this function as a piecewise function.
First: Define the variables.
Two things are involved in this function: age and cost.
Let $a$ be the age of the child.
Let $c$ be the cost of the meal.
As you can see, the cost of the meal depends on the age of the child.
This means that the cost is the dependent variable.
And the age of the child is the independent variable.
So, the cost of the meal is a function of the age of the child.
$c = f(a)$. We can write this as $c(a)$ pronounced as $c \: of \: a$
c(a) = \left \{\begin{aligned} & 0; && 0 < a ≤ 3 \\[2ex] & 5.99; && 3 < a ≤ 8 \\[2ex] & 6.99; && 8 < a ≤ 12 \end{aligned} \right.

Exercises
Use the piecewise function above and answer these questions.

(1.) Peter is 3 years old.
How much (excluding taxes) is the cost of his meal?

Peter eats free because he is $3$ years old. His age is included in the first "piece".
The cost of his meal is $\$0.00$(2.) Mary is 7 years old. How much (including taxes) is the cost of her meal? Assume Golden Corral charges a tax rate of 7.5%. Mary is$7$years old. So, her age is included in the second "piece". The cost of her meal is$\$5.99$

$7.5\% \\[3ex] = \dfrac{7.5}{100} \\[5ex] = 0.075 \\[3ex] 7.5\% \;\;tax\;\;on\;\;the\;\;cost \\[3ex] = 0.075 * 5.99 \\[3ex] = 0.44925 \\[3ex] Total\;\;cost = 5.99 + 0.44925 = 6.43925 \approx \$6.44 $Students should give more examples as seen in national parks, car rentals, and retail stores among others. They should cite their sources "properly". Teachers should emphasize the importance of citing sources accurately, and citing them in the correct format. What is a Piecewise Function? A piecewise function is a function consisting of sub-functions (pieces) defined on a sequence of intervals (domains). It is also known as a piecewise-defined function or hybrid function. The domain of each sub-function must not overlap. Ask students why the domains must not overlap. What would happen if the domains of any two sub-functions overlap? Some students may ask you that question first. If they do, ask them for their opinions. Residential Service Rates by Georgia Power; State of Georgia, USA As of the 30th day of December, 2018; the power rates for the Residential Service during the Summer Period (June - September) by Georgia Power is found here. We shall focus on the Residential Service Rates. These costs exclude taxes and other costs.  It is also written here for you: Basic Service:$10.00
First 650KWh:                 ¢5.7 per KWh
650 - 1000KWh:                ¢9.4 per KWh
Over 1000KWh:                 ¢9.7 per KWh


KWh means kilowatt hour.
$1$ KWh = $3600000$ J
$1$ kilowatt hour is equivalent to $3600000$ Joules.
The S.I (System International) unit of power is the Joule, $J$
The basic service fee is in dollars.
The rate of consumption is in cents.
We have to convert to the same unit.
We shall use the dollars (not the cents).
$\$1 = ¢100 \\[2ex] ¢100 = \$1 \\[2ex] ¢5.7 = \$0.057 \\[2ex] ¢9.4 = \$0.094 \\[2ex] ¢9.7 = \$0.097 $But, please wait a minute!!! That information is not "really" correct. Why would Georgia Power display incorrect information? The "Interactive Sample Bill" (hmmmm....it is not interactive though ☺☺☺) found here is also incorrect. Why? The correct information is found in the Georgia Power Bill Calculator of the Georgia Public Service Commission. The correct information is here It is great to know that the Georgia Public Service Commission developed a Power Bill calculator. We shall check our work with their calculator. And of course...we shall also check our work with my calculator.  The correct information is written here for you: Basic Service:$10.00
Tier                    Usage                   Cost per KWh
1st tier                up to 650KWh            $0.056582 2nd tier next 350KWh$0.093983
3rd tier                over 1000KWh            $0.097273  Teaching Moments (to promote critical thinking) Ask students to explain the differences between the information found in the Georgia Power website (the first one) and that found in the Georgia Public Service Commission (the second one). Students should also explain the differences based on the domains of each piece in both websites. What are the errors in the first one? Please specify the importance of not rounding intermediate calculations. Please specify the importance of rounding only the final answer to two decimal place (because it is dollars and cents). Calculate the power costs for the following consumption of power. (1.)$0$KWh (2.)$300$KWh (3.)$700$KWh (4.)$1000$KWh (5.)$1200$KWh Solution:$1st$Method: Manual/Arithmetic Method This application has three pieces. The basic service fee is not a piece. It must be paid whether one consumed any power or not. Let$p$= power (in KWh) Let$r$= cost (in dollars per KWh) (1.)$0$KWh falls in the first piece. Basic service fee = $$10.00 cost for 0 KWh @$$0.056582$ per KWh = $0 * 0.056582 = 0$
$10.00 + 0.00 = 10.00$
cost for $0$ KWh = $$10.00 (2.) 300 KWh falls in the first piece. Basic service fee =$$10.00$cost for$300$KWh @ $$0.056582 per KWh = 300 * 0.056582 = 16.9746 10.00 + 16.9746 = 26.9746 cost for 300 KWh =$$26.97$

(3.) $700$ KWh falls in the second piece.
Basic service fee = $$10.00 Before we use the second piece, we have to go through the first piece first. First Piece for 650 KWh cost for 650 KWh @$$0.056582$per KWh =$650 * 0.056582 = 36.7783700 - 650 = 50$We need to find the cost for the remaining$50$KWh That takes us to the second piece. Second Piece for$50$KWh cost for$50$KWh @ $$0.093983 per KWh = 50 * 0.093983 = 4.69915 10.00 + 36.7783 + 4.69915 = 51.47745 cost for 700 KWh =$$51.48$

(4.) $1000$ KWh falls in the second piece.
Basic service fee = $$10.00 Before we use the second piece, we have to go through the first piece first. First Piece for 650 KWh cost for 650 KWh @$$0.056582$per KWh =$650 * 0.056582 = 36.77831000 - 650 = 350$We need to find the cost for the remaining$350$KWh That takes us to the second piece. Second Piece for$350$KWh cost for$350$KWh @ $$0.093983 per KWh = 350 * 0.093983 = 32.89405 10.00 + 36.7783 + 32.89405 = 79.67235 cost for 1000 KWh =$$79.67$

(5.) $1200$ KWh falls in the third piece.
Basic service fee = $$10.00 Before we use the third piece, we have to go through the first piece and also through the second piece. First Piece for 650 KWh cost for 650 KWh @$$0.056582$per KWh =$650 * 0.056582 = 36.77831000 - 650 = 350$We need to find the cost for$350$KWh That takes us to the second piece. Second Piece for$350$KWh cost for$350$KWh @ $$0.093983 per KWh = 350 * 0.093983 = 32.89405 1200 - 1000 = 200 We need to find the cost for the remaining 200 KWh That takes us to the third piece. Third Piece for 200 KWh cost for 200 KWh @$$0.097273$ per KWh = $200 * 0.097273 = 19.4546$
$10.00 + 36.7783 + 32.89405 + 19.4546 = 99.12695$
cost for $1200$ KWh = $$99.13 Some students may ask if it is possible to have just one function that will find the cost for any consumption of power. Or is it possible to find the cost for the consumption of power that falls in the second piece, without having to go through the first piece? Those are really interesting questions! That is one of the reasons for studying piecewise functions ☺☺☺ Please specify the importance of not rounding intermediate calculations. Please specify the importance of rounding only the final answer to two decimal place (because it is dollars and cents). Solution: 2nd Method: Piecewise Function/Algebraic Method What if we have to calculate the power rates for "several" consumption of power? Do we have to solve this manually all the time? That will be time consuming! We can write it as a piecewise function and use each function for the consumption of power that correspond to that piece. Besides, writing it as a piecewise function helps us to write a computer program that will find the rate for any consumption of power. This application has three pieces. Let p = power consumed(in KWh) Let c = cost per KWh or power consumed (in dollars) c = f(p) This can be written as: c(p) For the first piece; Basic service fee =$$10.00$cost for$p$KWh @ $$0.056582 per KWh = p * 0.056582 = 0.056582p 10 + 0.056582p = 0.056582p + 10 c(p) = 0.056582p + 10 For the second piece; Basic service fee =$$10.00$
We have to "finish" with the first piece first
cost for $650$ KWh @ $$0.056582 per KWh = 650 * 0.056582 = 36.7783 10 + 36.7783 = 46.7783 Then, we can multiply the remaining consumption of power by 0.093983 c(p) = 46.7783 + 0.093983(p - 650) c(p) = 46.7783 + 0.093983p - 61.08895 c(p) = 0.093983p - 14.31065 For the third piece; Basic service fee =$$10.00$We have to "finish" with the first piece first cost for$650$KWh @ $$0.056582 per KWh = 650 * 0.056582 = 36.7783 10 + 36.7783 = 46.7783 Then we have to finish with the second piece next 1000 - 650 = 350 cost for 350 KWh @$$0.093983$ per KWh = $350 * 0.093983 = 32.89405$
$46.7783 + 32.89405 = 79.67235$
Then, we can multiply the remaining consumption of power by $0.097273$
$c(p) = 79.67235 + 0.097273(p - 1000)$
$c(p) = 79.67235 + 0.097273p - 97.273$
$c(p) = 0.097273p - 17.60065$

We can now write the piecewise function as:
$$c(p) = \begin{cases} 0.056582p + 10; & \quad 0 \leq p \leq 650 \\[3ex] 0.093983p - 14.31065; & \quad 650 \lt p \leq 1000 \\[3ex] 0.097273p - 17.60065; & \quad p \gt 1000 \end{cases}$$ Let us recalculate all the questions using the Piecewise Function method.

(1.) $0$ KWh falls in the first piece.

$c(p) = 0.056582p + 10 \\[3ex] c(0) = 0.056582(0) + 10 \\[3ex] = 0 + 10 \\[3ex] = 10 \\[3ex]$ cost for $0$ KWh = $$10.00 (2.) 300 KWh falls in the first piece.  c(p) = 0.056582p + 10 \\[3ex] c(300) = 0.056582(300) + 10 \\[3ex] = 16.9746 + 10 \\[3ex] = 26.9746 \\[3ex] = 26.97 \\[3ex]  cost for 300 KWh =$$26.97$(3.)$700$KWh falls in the second piece.$ c(p) = 0.093983p - 14.31065 \\[3ex] c(700) = 0.093983(700) - 14.31065 \\[3ex] = 65.7881 - 14.31065 \\[3ex] = 51.47745 \\[3ex] = 51.48 \\[3ex] $cost for$700$KWh = $$51.48 (4.) 1000 KWh falls in the second piece. c(p) = 0.093983p - 14.31065 \\[3ex] c(1000) = 0.093983(1000) - 14.31065 \\[3ex] = 93.983 - 14.31065 \\[3ex] = 79.67235 \\[3ex] = 79.67 \\[3ex] cost for 1000 KWh =$$79.67$

(5.) $1200$ KWh falls in the third piece.

$c(p) = 0.097273p - 17.60065 \\[3ex] c(1200) = 0.097273(1200) - 17.60065 \\[3ex] = 116.7276 - 17.60065 \\[3ex] = 99.12695 \\[3ex] = 99.13 \\[3ex]$ cost for $1200$ KWh = $$99.13 Which of the two methods do you prefer? What are your reasons? What are the pros and cons that you see for each method? Do you have any other method for solving Piecewise Function applications? Calculator for the Summer Residential Power Rates by Georgia Power, State of Georgia, USA Power Consumption and Monthly Bill Statement Please test the calculator and see the output. Complete all fields. Then, click "Bill Statement". • Power Consumption KWh KWh in • Monthly Bill Statement Calculator for the Winter Residential Power Rates by Georgia Power, State of Georgia, USA Power Consumption and Monthly Bill Statement Please test the calculator and see the output. Complete all fields. Then, click "Bill Statement". • Power Consumption KWh KWh in • Monthly Bill Statement Student Project: Power Bill Power Usage and Monthly Bill Statement Please review the calculations and test the calculator first. You may NOT use any of my examples even if the rates of the company have changed. On a first-come first-served basis: If this has not been done by another student: Please make sure you write it in the Projects Drafts forum that you are working on it so that another student will not work on it. (1.) I did the Power Bill: Summer Rate for Georgia Power. Any student may do the Power Bill: Winter Rate for Georgia Power (2.) Any student may do the Power Bill: Summer Rate for Alabama Power (3.) Any student may do the Power Bill: Winter Rate for Alabama Power For Mathematics and Information Technology/Computer Science Students: Midterm Project (1.) You may work as a group (peer tutor to teach and correct one another). However, this is an individual project. In other words, you will submit your own project. (2.) No two projects should be the same. (3.) Research any real-world case where piecewise function is used. (a.) All information used for this project should be verifiable on the direct website of the company/organization. (b.) Textbook examples are NOT allowed. (c.) Find any application that has at least 2 pieces, and has at least a function in each piece that includes the independent variable. (4.) Write the complete address of the direct page of the website where you found the application. (a.) *If the "direct" web address is too long, please shorten it by pasting the "complete web address" into www.tinyurl.com * *This is only for traditional students (onsite) students* *Generate a short address and write that address "as is".* (b.) For online students, please copy and paste the link "as is". (c.) Please set the link to open in a new window. (5.) I understand some of you do not want to type directly in the Blackboard editor using the Math Editor. You may: (a.) Show all your work on paper, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor. OR (b.) Show all your work in Microsoft Word, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor. Please DO NOT submit any attachment on Blackboard. It will not be clicked. It will not be opened. It will not be graded. (6.) If you need feedback on your project before submission, please submit your project as a draft in the Project Drafts forum on Blackboard. You may also send it to me as an attachment via email. I shall review and provide feedback. Draft projects are to be submitted in the Project Drafts forum. Draft projects are not graded. Actual projects that needs to be graded should be submittied in the actual Project forum. (7.) Research Skills: Cite your source properly. Use APA, MLA, or Chicago Manual of Style. Indicate the style you used. (8.) Writing Skills: Write or type the "main" application entirely. (9.) Mathematical Skills: Arithmetic Use random numbers to test the real-world application manually for each piece. Write down your results. (10.) Mathematical Skills: Algebra: Write a piecewise function for that application. Test the piecewise function with the same random numbers. The results should be the same. If the results are not the same, fix it.  Name: Your name Date: The date Instructor: Samuel Chukwuemeka Project: Power Bill: Residential Rates Company: Georgia Public Service Commission (for Georgia Power) (http://www.psc.state.ga.us/calc/electric/GPcalc.asp) Objectives: (1.) Calculate the winter/summer power bill of the residents of the State of Georgia within each range of specific power usage manually using Arithmetic method. (2.) Write a piecewise function of the residential rates. (3.) Recalculate the same power bill of the residents of the State of Georgia within each range of specific power usage algebraically using the Piecewise Function method. Information: Write the direct information from the direct website Arithmetic Method: Test each piece manually Piecewise Function: Write the piecewise function of the information Piecewise Function Method: Test the same each piece algebraically Citation: Indicate the type of citation format. Cite your source(s) accordingly. Student Sample (Math Part): The teacher should guide each student to the successful completion of the project. Let students know you are willing to help. For Information Technology/Computer Science Students: Midterm Project Minimum Requirements for Beginning C++ These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a console application. (3.) The Input/Output feature should be used. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (10.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Beginning VB.NET, Beginning C#, Beginning Java These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a desktop application. (3.) Set the MinimumBox property of the form to True We want to accommodate users with laptop/desktop smaller screen sizes too. They should have the ability to adjust your application to fit their screen sizes. (4.) The Input/Output feature should be used. Error Handling (5.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (6.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (8.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (9.) Use only tax in percent. Do not worry about tax in decimal. (10.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Advanced C++ These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information on the output. (2.) The application should be a console application. (3.) Input/Output feature should be used. (4.) Class should be used. (5.) Constructor(s) should be used. (6.) Property/Properties should be used. The class members: Initial Reading and the Final Reading should be private. (7.) Method(s) should be used. Error Handling (8.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (9.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (10.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (11.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (12.) Use only tax in percent. Do not worry about tax in decimal. (13.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (14.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Advanced VB.NET, Advanced C#, Advanced Java These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information on the output. (2.) The application should be a desktop application. (3.) Set the MinimumBox property of the form to True We want to accommodate users with laptop/desktop smaller screen sizes too. They should have the ability to adjust your application to fit their screen sizes. (4.) Input/Output feature should be used. (5.) Class should be used. (6.) Constructor(s) should be used. (7.) Property/Properties should be used. The class members: Initial Reading and the Final Reading should be private. (8.) Method(s) should be used. Error Handling (9.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (10.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (11.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (12.) Alert the user/Display appropriate error message to the user, if the Tax is negative. For the requirements for Numbers (9.), (10.), and (11.) Because the power consumption values are only nonnegative integers: Alternatively; you may use the NumericUpDown Control (www.docs.microsoft.com/en-us/dotnet/desktop/winforms/controls/numericupdown-control-windows-forms?view=netframeworkdesktop-4.8) The control will ensure that the user enters only nonnegative values (zero and positive values). (13.) Use only tax in percent. Do not worry about tax in decimal. (14.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (15.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for ASP.NET These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a web application. You may use Functional Programming or Object-oriented Programming. You may use ASP.NET Web Forms, ASP.NET Web Pages, ASP.NET MVC, or any other ASP.NET web platform. You may use C# or VB.NET (3.) The Input/Output feature should be used. Use nice HTML elements and CSS. Functionality is the most important factor. However, aesthetics and user-friendliness are also important factors in Web Design. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Include the URL of the web application (web address) in the documentation of your Math work. Please make sure the web application is accessible. The draft project should contain: documentation of Math work, the web application address, and the Project folder. The Project folder is the folder that is created when you create a new project. It contains all folders and files. Include all these in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. I shall review and provide feedback. (10.) When you are done (everything works well), please zip the entire project: (documentation of the Math that includes the URL, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. Minimum Requirements for JavaScript These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a web application. (3.) The Input/Output feature should be used. Use nice HTML elements and CSS. Functionality is the most important factor. However, aesthetics and user-friendliness are also important factors in Web Design. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Include the URL of the web application (web address) in the documentation of your Math work. Please make sure the web application is accessible. Ensure that you follow the best practices: link to the external CSS file in the head element and the link to the external JS file right before the closing body element. The draft project should contain: documentation of Math work that includes the URL. Include the draft project in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. I shall review and provide feedback. (10.) When you are done (everything works well), please submit the entire project: (documentation of the Math that includes the URL) in the actual Midterm Project forum of the Blackboard course. Optional Further Work Writing Skills: Submit a Reflection Journal. Include your challenges, and how you overcame those challenges. Technology Skills: Include penalties for late payments in your project. Write a mobile application for the project. Develop a mobile application that sends reminders to customers so they do not miss payments. Develop a rewards program that rewards customers who make payments on time. Water Rates by Calhoun County Water Authority; State of Alabama, USA As of the 7th day of July, 2018; the water rates by the Calhoun County Water Authority is found here We shall focus on the Residential Rates. These rates exclude taxes.  It is also written here for you: First 3,000 Gallons: 17.35 Minimum Per Month Next 2,000 Gallons: 5.24 per 1,000 Gallons Next 5,000 Gallons: 3.96 per 1,000 Gallons All over 10,000 Gallons: 3.10 per 1,000 Gallons  Calculate the water rates for the following consumption of water. (1.) 2500 gallons (2.) 3700 gallons (3.) 5000 gallons (4.) 7500 gallons (5.) 12000 gallons (6.) 4692 gallons (7.) 6456 gallons Solution: 1st Method: Manual/Arithmetic Method This application has four pieces. Let g = gallons of water (in gallons) Let r = rate (in dollars per gallons) (1.) 2500 gallons falls in the first piece. rate for 2500 gallons @$$17.35$= $$17.35 (2.) 3700 gallons falls in the second piece. Before we use the second piece, we have to go through the first piece first. rate for 3000 gallons @$$17.35$ = $$17.35 3700 - 3000 = 700 We need to find the rate for the remaining 700 gallons The first piece (for 3000 gallons) is a constant rate. It is a flat fee. However, the second piece is$$5.24$per$1000$gallons The second piece is $$5.24 per 1000 (not per 700) gallons But, we have 700 (not 1000 gallons remaining). What do we do? We have to use Proportional Reasoning Method to calculate the rate per gallons (rather than using the rate per thousand gallons) Remember: per gallon means for 1 gallon; and per 1000 gallons means for a thousand gallons Let us set up the Proportional Reasoning Let x be the cost per gallon  dollars gallons 5.24 1000 x 1  This means that:$$ \dfrac{5.24}{x} = \dfrac{1000}{1} \\[5ex] 1000 * x = 5.24 * 1 \\[3ex] 1000 * x = 5.24 \\[3ex] x = \dfrac{5.24}{1000} \\[5ex] x = 0.00524 $$Similarly;$$ \dfrac{3.96}{x} = \dfrac{1000}{1} \\[5ex] 1000 * x = 3.96 * 1 \\[3ex] 1000 * x = 3.96 \\[3ex] x = \dfrac{3.96}{1000} \\[5ex] x = 0.00396 $$And;$$ \dfrac{3.10}{x} = \dfrac{1000}{1} \\[5ex] 1000 * x = 3.1 * 1 \\[3ex] 1000 * x = 3.1 \\[3ex] x = \dfrac{3.1}{1000} \\[5ex] x = 0.0031 $$Can we re-write the application?  First 3,000 Gallons: 17.35 Minimum Per Month Next 2,000 Gallons: 0.00524 per gallon Next 5,000 Gallons: 0.00396 per gallon All over 10,000 Gallons: 0.0031 per gallon  Ask students if they understood how the rates per gallon were calculated. So, back to completing the second question: rate for 700 gallons @ 0.00524 per gallon = 0.00524 * 700 =$$3.668$
Please do not approximate intermediate calculations especially if it deals with money!
rate for $3700$ gallons @ = 17.35 + 3.668 = 21.018
Now, you can round your final answer to the nearest cent.
NOTE: If your professor does not want you to round, do not round.
rate for $3700$ gallons = $$21.02 (3.) 5000 gallons falls in the second piece. Before we use the second piece, we have to go through the first piece first. rate for 3000 gallons @$$17.35$= $$17.35 5000 - 3000 = 2000 rate for 2000 gallons @ 0.00524 per gallon = 0.00524 * 2000 =$$10.48$
rate for $5000$ gallons @ = 17.35 + 10.48 = 27.83
rate for $5000$ gallons = $$27.83 (4.) 7500 gallons falls in the third piece. Before we use the third piece, we have to go through the first and second pieces. rate for 3000 gallons @$$17.35$= $$17.35 7500 - 3000 = 4500 rate for 2000 gallons @ 0.00524 per gallon = 0.00524 * 2000 =$$10.48$
$4500 - 2000 = 2500$
rate for $2500$ gallons @ $0.00396 per gallon =$0.00396 * 2500$= $$9.90 rate for 7500 gallons @ = 17.35 + 10.48 + 9.90 = 37.73 rate for 7500 gallons =$$37.73$

(5.) $12000$ gallons falls in the fourth piece.
Before we use the third piece, we have to go through the first, second, and third pieces.
rate for $3000$ gallons @ $$17.35 =$$17.3512000 - 3000 = 9000$rate for$2000$gallons @$0.00524 per gallon = $0.00524 * 2000$ = $$10.48 9000 - 2000 = 7000 rate for 5000 gallons @ 0.00396 per gallon = 0.00396 * 5000 =$$19.807000 - 5000 = 2000$rate for$2000$gallons @$ per gallon = $0.0031 * 2000$ = $$6.20 rate for 12000 gallons @ = 17.35 + 10.48 + 19.80 + 6.20 = 53.83 rate for 12000 gallons =$$53.83$(6.)$4692$gallons falls in the second piece. Before we use the second piece, we have to go through the first piece first. rate for$3000$gallons @ $$17.35 =$$17.35$
$4692 - 3000 = 1692$
rate for $1692$ gallons @ $0.00524 per gallon =$0.00524 * 1692$= $$8.86608 rate for 4692 gallons @ = 17.35 + 8.86608 = 26.21608 rate for 4692 gallons =$$26.22$

(7.) $6456$ gallons falls in the third piece.
Before we use the third piece, we have to go through the first and second pieces.
rate for $3000$ gallons @ $$17.35 =$$17.356456 - 3000 = 3456$rate for$2000$gallons @$0.00524 per gallon = $0.00524 * 2000$ = $$10.48 3456 - 2000 = 1456 rate for 1456 gallons @ 0.00396 per gallon = 0.00396 * 1456 =$$5.76576$rate for$6456$gallons @ = 17.35 + 10.48 + 5.76576 = 33.59576 rate for$6456$gallons = $$33.60 Some students may ask if it is possible to have just one function that will find the rate for any gallon(s) of water?. Or is it possible to find the rate for gallons of water that is contained in the second piece, without having to go through the first piece? Solution: 2nd Method: Piecewise Function/Algebraic Method What if we have to calculate the water rates for "several" gallons of water? Do we have to solve this manually all the time? That will be time consuming! We can write it as a piecewise function and use each function for the number of gallons that correspond to that piece. Besides, writing it as a piecewise function helps us to write a computer program that will find the rate for any gallon of water. This application has four pieces. Let g = gallons of water (in gallons) Let r = rate (in dollars per gallons) r = f(g) This can be written as: r(g) For the first piece; r(g) =$$17.35$

For the second piece;
We have to "finish" with the first piece first
Then, we can multiply the remaining gallons of water by $0.00524$
$r(g) = 17.35 + 0.00524(g - 3000)$
$r(g) = 17.35 + 0.00524g - 15.72$
$r(g) = 0.00524g + 1.63$

For the third piece;
We have to "finish" the second piece first
Then, we can multiply the remaining gallons of water by $0.00396$
What is the complete gallons for the second piece? - It is $5000$
In other words, $5000$ is the end point for the second piece. $5000$ is included.
Let us find the rate for that end point, $5000$
$r(g) = 0.00524(5000) + 1.63$
$r(g) = 26.2 + 1.63 = 27.83$
So, $$27.83 is the most that can be charged for the second piece. Any remaining gallons over 5000 would be multiplied by 0.00396 r(g) = 27.83 + 0.00396(g - 5000) r(g) = 27.83 + 0.00396g - 19.8 r(g) = 0.00396g + 8.03 For the fourth piece; We have to "finish" the third piece first Then, we can multiply the remaining gallons of water by 0.0031 What is the complete gallons for the second piece? - It is 10000 In other words, 10000 is the end point for the third piece. 10000 is included. Let us find the rate for that end point, 10000 r(g) = 0.00396(10000) + 8.03 r(g) = 39.6 + 8.03 = 47.63 So,$$47.63$is the most that can be charged for the third piece. Any remaining gallons over$10000$would be multiplied by$0.0031r(g) = 47.63 + 0.0031(g - 10000)r(g) = 47.63 + 0.0031g - 31r(g) = 0.0031g + 16.63$We can now write the piecewise function as: $$r(g) = \begin{cases} 17.35; & \quad 0 \leq g \leq 3000 \\[2ex] 0.00524g + 1.63; & \quad 3000 \lt g \leq 5000 \\[2ex] 0.00396g + 8.03; & \quad 5000 \lt g \leq 10000 \\[2ex] 0.0031g + 16.63; & \quad g \gt 10000 \end{cases}$$ Let us recalculate all the questions using the Piecewise Function method. (1.)$2500$gallons falls in the first piece. The rate for the first piece is $$17.35 \therefore the rate for 2500 gallons of water =$$17.35$

(2.) $3700$ gallons falls in the second piece.
The rate for the second piece is $0.00524g + 1.63$
For $g = 3700$, $r = 0.00524(3700) + 1.63$
$r = 19.388 + 1.63$
$r = 21.018$
$\therefore$ the rate for $3700$ gallons of water = $$21.02 (3.) 5000 gallons falls in the second piece. The rate for the second piece is 0.00524g + 1.63 For g = 5000, r = 0.00524(5000) + 1.63 r = 26.2 + 1.63 r = 27.83 \therefore the rate for 5000 gallons of water =$$27.83$(4.)$7500$gallons falls in the third piece. The rate for the third piece is$0.00396g + 8.03$For$g = 7500$,$r = 0.00396(7500) + 8.03r = 29.7 + 8.03r = 37.73\therefore$the rate for$7500$gallons of water = $$37.73 (5.) 12000 gallons falls in the fourth piece. The rate for the fourth piece is 0.0031g + 16.63 For g = 12000, r = 0.0031(12000) + 16.63 r = 37.2 + 16.63 r = 53.83 \therefore the rate for 12000 gallons of water =$$53.83$

(6.) $4692$ gallons falls in the second piece.
The rate for the second piece is $0.00524g + 1.63$
For $g = 4692$, $r = 0.00524(4692) + 1.63$
$r = 24.58608 + 1.63$
$r = 26.21608$
$\therefore$ the rate for $4692$ gallons of water = $$26.22 (7.) 6456 gallons falls in the third piece. The rate for the third piece is 0.00396g + 8.03 For g = 6456, r = 0.00396(6456) + 8.03 r = 25.56576 + 8.03 r = 33.59576 \therefore the rate for 6456 gallons of water =$$33.60$Which of the two methods do you prefer? What are your reasons? What are the pros and cons that you see for each method? Do you have any other method for solving Piecewise Function applications? Calculator for the Water Rates by Calhoun County Water Authority, State of Alabama, USA Water Usage and Monthly Bill Statement Please test the calculator and see the output. Complete all fields. Then, click "Bill Statement". • Water Usage gallons gallons in • Monthly Bill Statement Student Project: Water Bill Water Usage and Monthly Bill Statement Please review the calculations and test the calculator first. You may NOT use any of my examples even if the rates of the company have changed. For Mathematics and Information Technology/Computer Science Students: Midterm Project (1.) You may work as a group (peer tutor to teach and correct one another). However, this is an individual project. In other words, you will submit your own project. (2.) No two projects should be the same. (3.) Research any real-world case where piecewise function is used. (a.) All information used for this project should be verifiable on the direct website of the company/organization. (b.) Textbook examples are NOT allowed. (c.) Find any application that has at least$2$pieces, and has at least a function in each piece that includes the independent variable. (4.) Write the complete address of the direct page of the website where you found the application. (a.) *If the "direct" web address is too long, please shorten it by pasting the "complete web address" into www.tinyurl.com * *This is only for traditional students (onsite) students* *Generate a short address and write that address "as is".* (b.) For online students, please copy and paste the link "as is". (c.) Please set the link to open in a new window. (5.) I understand some of you do not want to type directly in the Blackboard editor using the Math Editor. You may: (a.) Show all your work on paper, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor. OR (b.) Show all your work in Microsoft Word, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor. Please DO NOT submit any attachment on Blackboard. It will not be clicked. It will not be opened. It will not be graded. (6.) If you need feedback on your project before submission, please submit your project as a draft in the Project Drafts forum on Blackboard. You may also send it to me as an attachment via email. I shall review and provide feedback. Draft projects are to be submitted in the Project Drafts forum. Draft projects are not graded. Actual projects that needs to be graded should be submittied in the actual Project forum. (7.) Research Skills: Cite your source properly. Use APA, MLA, or Chicago Manual of Style. Indicate the style you used. (8.) Writing Skills: Write or type the "main" application entirely. (9.) Mathematical Skills: Arithmetic Use random numbers to test the real-world application manually for each piece. Write down your results. (10.) Mathematical Skills: Algebra: Write a piecewise function for that application. Test the piecewise function with the same random numbers. The results should be the same. If the results are not the same, fix it.  Name: Your name Date: The date Instructor: Samuel Chukwuemeka Project: Water Bill: Residential Rates Company: Calhoun County Water Authority (https://calhouncwa.com/rates.htm) Objectives: (1.) Calculate the water bill of the residents of Calhoun County in the State of Alabama within each range of specific water usage manually using Arithmetic method. (2.) Write a piecewise function of the residential rates. (3.) Recalculate the same water bill of the residents of Calhoun County in the State of Alabama within each range of specific water usage algebraically using the Piecewise Function method. Information: Write the direct information from the direct website Arithmetic Method: Test each piece manually Piecewise Function: Write the piecewise function of the information Piecewise Function Method: Test the same each piece algebraically Citation: Indicate the type of citation format. Cite your source accordingly. Student Sample (Math Part): The teacher should guide each student to the successful completion of the project. Let students know you are willing to help. For Information Technology/Computer Science Students: Midterm Project Minimum Requirements for Beginning C++ These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a console application. (3.) The Input/Output feature should be used. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (10.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Beginning VB.NET, Beginning C#, Beginning Java These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a desktop application. (3.) Set the MinimumBox property of the form to True We want to accommodate users with laptop/desktop smaller screen sizes too. They should have the ability to adjust your application to fit their screen sizes. (4.) The Input/Output feature should be used. Error Handling (5.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (6.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (8.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (9.) Use only tax in percent. Do not worry about tax in decimal. (10.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Advanced C++ These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information on the output. (2.) The application should be a console application. (3.) Input/Output feature should be used. (4.) Class should be used. (5.) Constructor(s) should be used. (6.) Property/Properties should be used. The class members: Initial Reading and the Final Reading should be private. (7.) Method(s) should be used. Error Handling (8.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (9.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (10.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (11.) Alert the user/Display appropriate error message to the user, if the Tax is negative. For the requirements for Numbers (9.), (10.), and (11.) Because the power consumption values are only nonnegative integers: Alternatively; you may use the NumericUpDown Control (www.docs.microsoft.com/en-us/dotnet/desktop/winforms/controls/numericupdown-control-windows-forms?view=netframeworkdesktop-4.8) The control will ensure that the user enters only nonnegative values (zero and positive values). (12.) Use only tax in percent. Do not worry about tax in decimal. (13.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (14.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. Student: Mr. C, what do you mean? Teacher: When you submit your project folder; Mr. C may: Click the Project folder, then the bin folder, then the Debug folder, then run the .exe file. (Project --> bin --> Debug --> .exe file) The file with the .exe extension is known as the executable file. Student: May I ask what you do with the execuatable files? Teacher: Good question. This is the reason: Look at the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. So, it is recommended you include the title of your project in the main file: .cpp file FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for Advanced VB.NET, Advanced C#, Advanced Java These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information on the output. (2.) The application should be a desktop application. (3.) Set the MinimumBox property of the form to True We want to accommodate users with laptop/desktop smaller screen sizes too. They should have the ability to adjust your application to fit their screen sizes. (4.) Input/Output feature should be used. (5.) Class should be used. (6.) Constructor(s) should be used. (7.) Property/Properties should be used. The class members: Initial Reading and the Final Reading should be private. (8.) Method(s) should be used. Error Handling (9.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (10.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (11.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (12.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (13.) Use only tax in percent. Do not worry about tax in decimal. (14.) Make sure your executable file runs by itself outside the project folder If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. You may also upload them directly if you prefer. I shall review and provide feedback. If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project. When you submit it, I shall review and provide feedback. If it does not run, then you need to fix it. If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you. (15.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. This is the reason: Please review the Students section: Samples of Students Work You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students. FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students). However, I will include your first name on my website if I use your work. Minimum Requirements for ASP.NET These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a web application. You may use Functional Programming or Object-oriented Programming. You may use ASP.NET Web Forms, ASP.NET Web Pages, ASP.NET MVC, or any other ASP.NET web platform. You may use C# or VB.NET (3.) The Input/Output feature should be used. Use nice HTML elements and CSS. Functionality is the most important factor. However, aesthetics and user-friendliness are also important factors in Web Design. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Include the URL of the web application (web address) in the documentation of your Math work. Please make sure the web application is accessible. The draft project should contain: documentation of Math work, the web application address, and the Project folder. The Project folder is the folder that is created when you create a new project. It contains all folders and files. Include all these in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. I shall review and provide feedback. (10.) When you are done (everything works well), please zip the entire project: (documentation of the Math that includes the URL, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course. Minimum Requirements for JavaScript These are the minimum requirements. Please be creative. (1.) Please use appropriate naming for your project application. The application should display at least the same output of my calculator. That implies that you should test my calculator to see the output. Your application may include more information. (2.) The application should be a web application. (3.) The Input/Output feature should be used. Use nice HTML elements and CSS. Functionality is the most important factor. However, aesthetics and user-friendliness are also important factors in Web Design. Error Handling (4.) Alert the user/Display an appropriate error message to the user, if the Final Reading is less than the Initial Reading. (5.) Alert the user/Display an appropriate error message to the user, if the Initial Reading is negative. (6.) Alert the user/Display appropriate error message to the user, if the Final Reading is negative. (7.) Alert the user/Display appropriate error message to the user, if the Tax is negative. (8.) Use only tax in percent. Do not worry about tax in decimal. (9.) Include the URL of the web application (web address) in the documentation of your Math work. Please make sure the web application is accessible. Ensure that you follow the best practices: link to the external CSS file in the head element and the link to the external JS file right before the closing body element. The draft project should contain: documentation of Math work that includes the URL. Include the draft project in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email. I shall review and provide feedback. (10.) When you are done (everything works well), please submit the entire project: (documentation of the Math that includes the URL) in the actual Midterm Project forum of the Blackboard course. Optional Further Work Writing Skills: Submit a Reflection Journal. Include your challenges, and how you overcame those challenges. Technology Skills: Include penalties for late payments in your project. Write a mobile application for the project. Develop a mobile application that sends reminders to customers so they do not miss payments. Develop a rewards program that rewards customers who make payments on time. Federal Income Tax Rates:$2018$Another important real-world application of Piecewise Functions is in the filing of federal income taxes. We shall illustrate this application by filing the "Single" option for the$2018$federal tax return. We shall design a calculator for these taxes. We shall verify our calculations with the calculators of some tax companies. For the simple calculations (only taxes), we shall verify it using the: calculator from TaxAct Let us define some important terms used in Income Taxes. The gross income is the total yearly income. This is the total income earned in a year. It is the total pre-tax earnings for the year. Let the gross income =$GI$Sometimes, there are certain portions of the gross income that is not taxed. In other words, there are certain untaxed portions of the gross income. Those untaxed portions of the gross income are known as deductions or adjustments. Let the adjustments =$A$The difference between the gross income and the adjustments is known as the adjusted gross income Let the adjusted gross income =$AGI$The adjusted gross income is the income after allowable tax deductions. The information used for the$2018$tax rates, standard deductions, and exemptions is found in these websites: (1.) Bankrate (2.) Forbes Ask students to compare and contrast the two tables. The information from the first website (Bankrate) is summarized here. We shall work with this one first. Tax Rate Single Head of household Married Filing Jointly Or Qualifying Widow Married Filing Separately$10\%$Up to$\$9,525$ Up to $\$13,600$Up to$\$19,050$ Up to $\$9,52512\%\$9,526 \:\:to\:\: \$38,700\$13,601 \:\:to\:\: \$51,800\$19,051 \:\:to\:\: \$77,400\$9,526 \:\:to\:\: \$38,70022\%\$38,701 \:\:to\:\: \$82,500\$51,801 \:\:to\:\: \$82,500\$77,401 \:\:to\:\: \$165,000\$38,701 \:\:to\:\: \$82,50024\%\$82,501 \:\:to\:\: \$157,500\$82,501 \:\:to\:\: \$157,500\$165,001 \:\:to\:\: \$315,000\$82,501 \:\:to\:\: \$157,00032\%\$157,501 \:\:to\:\: \$200,000\$157,501 \:\:to\:\: \$200,000\$315,001 \:\:to\:\: \$400,000\$157,001 \:\:to\:\: \$200,00035\%\$200,001 \:\:to\:\: \$500,000\$200,001 \:\:to\:\: \$500,000\$400,001 \:\:to\:\: \$600,000\$200,001 \:\:to\:\: \$300,00037\%\$500,001 \:\:or\:\: more$ $\$500,001 \:\:or\:\: more\$600,001 \:\:or\:\: more$ $\$300,001 \:\:or\:\: more$Let us calculate the taxes for the filing "Single" option. We shall test each piece. Calculate the taxes for single individuals whose taxable incomes are: (1.)$\$7,000.00$
(2.) $\$12,575.00$(3.)$\$43,750.00$
(4.) $\$120,327.00$(5.)$\$165,428.00$
(6.) $\$234,543.00$(7.)$\$700,712.00$

Simplify the percents.
$10\% = \dfrac{10}{100} = 0.1 \\[5ex] 12\% = \dfrac{12}{100} = 0.12 \\[5ex] 22\% = \dfrac{22}{100} = 0.22 \\[5ex] 24\% = \dfrac{24}{100} = 0.24 \\[5ex] 32\% = \dfrac{32}{100} = 0.32 \\[5ex] 35\% = \dfrac{35}{100} = 0.35 \\[5ex] 37\% = \dfrac{37}{100} = 0.37$
Solution: $1st$ Method: Manual/Arithmetic Method
(1.) $\$7,000.00$falls in the first piece. tax for$\$7000.00$ income @ $10\%$ per $\$$earned = 7000 * 0.1 = 700 tax for taxable income of \7,000.00 = \700.00 (2.) \12,575.00 falls in the second piece. Before we use the second piece, we have to go through the first piece first. First Piece for \9525.00 9525.00 of the 12575.00 is taxed at 10\% tax for \9525.00 income @ 10\% per \$$ earned =$9525.00 * 0.1 = 952.50$We are done with the maximum taxable income that can be taxed at the first piece of$10\%$We have to move on to the second piece.$12575.00 - 9525.00 = 3050.00$The rest of the$\$3050.00$ is taxed at $12\%$
Second Piece for $\$3050.00$tax for$\$3050.00$ income @ $12\%$ per $\$$earned = 3050.00 * 0.12 = 366.00 952.50 + 366.00 = 1318.50 tax for taxable income of \12,575.00 = \1,318.50 (3.) \43,750.00 falls in the third piece. Before we use the third piece, we have to go through the first and second pieces. First Piece for \9525.00 9525.00 of the 12575.00 is taxed at 10\% tax for \9525.00 income @ 10\% per \$$ earned =$9525.00 * 0.1 = 952.50$We are done with the maximum taxable income that can be taxed at the first piece of$10\%$We have to move on to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. Student: So, do we need to subtract$9525.00$from$43750.28$Teacher: No, we do not. Here is the thing. We know already that$43750.28$falls in the third tax bracket. Student: That is correct. Teacher:$9,525$of that money is taxed at$10\%$Student: Okay... Teacher: Any money above$9525$but not exceeding$38700$is taxed at$12\%$Not all the money (43750.00 - 9525 = 34225.00) is taxed at$12\%$Let us look at it this way For$43750.28[0, 9525]$is taxed at$10\%(9525, 38700]$is taxed at$12\%(38700, 43750.28]$is taxed at$22\%$Do you realize the mistake that would have been made if$34225.00$was taxed at$12\%$Student: Yes, the U,S government would lose money. Teacher: That is right...and we do not ... Student: want them to lose money. Teacher: Correct. That money could be used to help the poor. Student: I hope they help poor people. There is a high rate of hunger and poverty in the world. Teacher: I hope and pray so too. So, as you can see: The range of$9525 - 0 = 9525$is taxed at$10\%$Student: The range of$38700 - 9525 = 29175$is taxed at$12\%$Teacher: Correct! Go ahead... Student: and the range of$43750.00 - 38700 = 5050.00$is taxed at$22\%$Teacher: Perfecto!$38700.00 - 9525.00 = 29175.00\$29175.00$ is taxed at $12\%$
Second Piece for $\$29175.00$tax for$\$29175.00$ income @ $12\%$ per $\$$earned = 29175.00 * 0.12 = 3501.00 We are done with the maximum taxable income that can be taxed at the second piece of 12\% We have to move on to the third piece. 43750.00 - 38700.00 = 5050.00 The rest of the \5050.00 is taxed at 22\% Third Piece for \14575.00 tax for \5050.00 income @ 22\% per \$$ earned =$5050.00 * 0.22 = 1111.00952.50 + 3501.00 + 1111.00 = 5564.50$tax for taxable income of$\$43,750.00$ = $\$5,564.50$(4.)$\$120, 327.00$ falls in the fourth piece.
Before we use the fourth piece, we have to go through the first, second, and third pieces.
First Piece for $\$9525.009525.00$of the$12575.00$is taxed at$10\%$tax for$\$9525.00$ income @ $10\%$ per $\$$earned = 9525.00 * 0.1 = 952.50 We are done with the maximum taxable income that can be taxed at the first piece of 10\% We move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. 38700.00 - 9525.00 = 29175.00 \29175.00 is taxed at 12\% Second Piece for \29175.00 tax for \29175.00 income @ 12\% per \$$ earned =$29175.00 * 0.12 = 3501.00$We are done with the maximum taxable income that can be taxed at the second piece of$12\%$We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate.$82500.00 - 38700.00 = 43800.00\$43800.00$ is taxed at $22\%$
Third Piece for $\$43800.00$tax for$\$43800.00$ income @ $22\%$ per $\$$earned = 43800.00 * 0.22 = 9636.00 We are done with the maximum taxable income that can be taxed at the third piece of 22\% We move to the fourth piece. 120327.00 - 82500.00 = 37827.00 The rest of the \37827.00 is taxed at 24\% Fourth Piece for \37827.00 tax for \37827.00 income @ 24\% per \$$ earned =$37827.00 * 0.24 = 9078.48952.50 + 3501.00 + 9636.00 + 9078.48 = 23167.98$tax for taxable income of$\$120,327.00$ = $\$23,167.98$(5.)$\$165, 428.00$ falls in the fifth piece.
Before we use the fifth piece, we have to go through the first, second, third, and fourth pieces.
First Piece for $\$9525.009525.00$of the$12575.00$is taxed at$10\%$tax for$\$9525.00$ income @ $10\%$ per $\$$earned = 9525.00 * 0.1 = 952.50 We are done with the maximum taxable income that can be taxed at the first piece of 10\% We move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. 38700.00 - 9525.00 = 29175.00 \29175.00 is taxed at 12\% Second Piece for \29175.00 tax for \29175.00 income @ 12\% per \$$ earned =$29175.00 * 0.12 = 3501.00$We are done with the maximum taxable income that can be taxed at the second piece of$12\%$We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate.$82500.00 - 38700.00 = 43800.00\$43800.00$ is taxed at $22\%$
Third Piece for $\$43800.00$tax for$\$43800.00$ income @ $22\%$ per $\$$earned = 43800.00 * 0.22 = 9636.00 We are done with the maximum taxable income that can be taxed at the third piece of 22\% We move to the fourth piece. We need to calculate the range of taxable income that should be taxed at the fourth tax rate. 157500.00 - 82500.00 = 75000.00 \75000.00 is taxed at 24\% Fourth Piece for \75000.00 tax for \75000.00 income @ 24\% per \$$ earned =$75000.00 * 0.24 = 18000.00$We are done with the maximum taxable income that can be taxed at the fourth piece of$24\%$We move to the fifth piece.$165428.00 - 157500.00 = 7928.00$The rest of the$\$7928.00$ is taxed at $32\%$
Fifth Piece for $\$7928.00$tax for$\$7928.00$ income @ $32\%$ per $\$$earned = 7928.00 * 0.32 = 2536.96 952.50 + 3501.00 + 9636.00 + 18000 + 2536.96 = 34626.46 tax for taxable income of \165,428.00 = \34,626.46 (6.) \234,543.00 falls in the sixth piece. Before we use the sixth piece, we have to go through the first, second, third, fourth, and fifth pieces. First Piece for \9525.00 9525.00 of the 12575.00 is taxed at 10\% tax for \9525.00 income @ 10\% per \$$ earned =$9525.00 * 0.1 = 952.50$We are done with the maximum taxable income that can be taxed at the first piece of$10\%$We move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate.$38700.00 - 9525.00 = 29175.00\$29175.00$ is taxed at $12\%$
Second Piece for $\$29175.00$tax for$\$29175.00$ income @ $12\%$ per $\$$earned = 29175.00 * 0.12 = 3501.00 We are done with the maximum taxable income that can be taxed at the second piece of 12\% We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate. 82500.00 - 38700.00 = 43800.00 \43800.00 is taxed at 22\% Third Piece for \43800.00 tax for \43800.00 income @ 22\% per \$$ earned =$43800.00 * 0.22 = 9636.00$We are done with the maximum taxable income that can be taxed at the third piece of$22\%$We move to the fourth piece. We need to calculate the range of taxable income that should be taxed at the fourth tax rate.$157500.00 - 82500.00 = 75000.00\$75000.00$ is taxed at $24\%$
Fourth Piece for $\$75000.00$tax for$\$75000.00$ income @ $24\%$ per $\$$earned = 75000.00 * 0.24 = 18000.00 We are done with the maximum taxable income that can be taxed at the fourth piece of 24\% We move to the fifth piece. We need to calculate the range of taxable income that should be taxed at the fifth tax rate. 200000.00 - 157500.00 = 42500.00 \42500.00 is taxed at 32\% Fifth Piece for \42500.00 tax for \42500.00 income @ 32\% per \$$ earned =$42500.00 * 0.32 = 13600.00$We are done with the maximum taxable income that can be taxed at the fifth piece of$32\%$We move to the sixth piece.$234543.00 - 200000.00 = 34543.00$The rest of the$\$34543.00$ is taxed at $35\%$
Sixth Piece for $\$34543.00$tax for$\$34543.00$ income @ $35\%$ per $\$$earned = 34543.00 * 0.35 = 12090.05 952.50 + 3501.00 + 9636.00 + 18000 + 13600 + 12090.05 = 57779.55 tax for taxable income of \234,543.00 = \57,779.55 (7.) \700,712.00 falls in the seventh piece. Before we use the seventh piece (last piece), we have to go through the previous six pieces in order. First Piece for \9525.00 9525.00 of the 12575.00 is taxed at 10\% tax for \9525.00 income @ 10\% per \$$ earned =$9525.00 * 0.1 = 952.50$We are done with the maximum taxable income that can be taxed at the first piece of$10\%$We move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate.$38700.00 - 9525.00 = 29175.00\$29175.00$ is taxed at $12\%$
Second Piece for $\$29175.00$tax for$\$29175.00$ income @ $12\%$ per $\$$earned = 29175.00 * 0.12 = 3501.00 We are done with the maximum taxable income that can be taxed at the second piece of 12\% We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate. 82500.00 - 38700.00 = 43800.00 \43800.00 is taxed at 22\% Third Piece for \43800.00 tax for \43800.00 income @ 22\% per \$$ earned =$43800.00 * 0.22 = 9636.00$We are done with the maximum taxable income that can be taxed at the third piece of$22\%$We move to the fourth piece. We need to calculate the range of taxable income that should be taxed at the fourth tax rate.$157500.00 - 82500.00 = 75000.00\$75000.00$ is taxed at $24\%$
Fourth Piece for $\$75000.00$tax for$\$75000.00$ income @ $24\%$ per $\$$earned = 75000.00 * 0.24 = 18000.00 We are done with the maximum taxable income that can be taxed at the fourth piece of 24\% We move to the fifth piece. We need to calculate the range of taxable income that should be taxed at the fifth tax rate. 200000.00 - 157500.00 = 42500.00 \42500.00 is taxed at 32\% Fifth Piece for \42500.00 tax for \42500.00 income @ 32\% per \$$ earned =$42500.00 * 0.32 = 13600.00$We are done with the maximum taxable income that can be taxed at the fifth piece of$32\%$We move to the sixth piece. We need to calculate the range of taxable income that should be taxed at the sixth tax rate.$500000.00 - 200000.00 = 300000.00\$300000.00$ is taxed at $35\%$
Sixth Piece for $\$300000.00$tax for$\$300000.00$ income @ $35\%$ per $\$$earned = 300000.00 * 0.35 = 105000.00 We are done with the maximum taxable income that can be taxed at the sixth piece of 35\% We move to the seventh piece. 700712.00 - 500000.00 = 200712.00 The rest of the \200712.00 is taxed at 37\% Seventh Piece for \200712.00 tax for \200712.00 income @ 37\% per \$$ earned =$200712.00 * 0.37 = 74263.44952.50 + 3501.00 + 9636.00 + 18000 + 13600 + 105000 + 74263.44 = 224952.94$tax for taxable income of$\$700,712.00$ = $\$224,952.94$Some students may ask if it is possible to have just one function that will calculate the tax for any taxable income. Or is it possible to find the tax for a taxable income that falls in the second piece, without having to go through the first piece? Those are really interesting questions! That is one of the reasons for studying piecewise functions ☺☺☺ Please specify the importance of not rounding intermediate calculations. Please specify the importance of rounding only the final answer to two decimal place (because it is dollars and cents). Solution:$2nd$Method: Piecewise Function/Algebraic Method What if we have to calculate the taxes for "several" taxable incomes? Do we have to solve this manually all the time? That will be time consuming! We can write it as a piecewise function and use each function to calculate the taxes that corresponds to each taxable income. Besides, writing it as a piecewise function helps us to write a computer program that will calculate the taxes for any amount of taxable income. Define the variables. Let$p$= taxable income (in$\$$) Let t = taxes (in \$$)
The taxes paid is a function of the income earned.
Taxes is the dependent variable.
Taxable income is the independent variable.
$t = f(p)$
We can also write is as $t(p)$
This application has seven pieces.

For the first piece;
tax for $\$p$income @$10\%$per$\$$earned = p * 0.1 = 0.1p t(p) = 0.1p For the second piece; We have to "finish" with the first piece first First Piece for \9525.00 tax for \9525 income @ 10\% per \$$ earned = $9525 * 0.1 = 952.5$
Then, we move to the second piece.
Second Piece for $\$p - 9525.00$The remaining income,$(p - 9525)$is taxed at$12\%$So, we have to multiply the remaining income by$0.12t(p) = 952.5 + 0.12(p - 9525)t(p) = 952.5 + 0.12p - 1143t(p) = 0.12p - 190.5$For the third piece; We have to "finish" with the first and second pieces First Piece for$\$9525.00$
tax for $\$9525$income @$10\%$per$\$$earned = 9525 * 0.1 = 952.5 Then, we move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. Please review the scenario in the Manual/Arithmetic Method 38700.00 - 9525.00 = 29175.00 \29175.00 is taxed at 12\% Second Piece for \29175.00 tax for \29175.00 income @ 12\% per \$$ earned = $29175.00 * 0.12 = 3501.00$
We are done with the maximum taxable income that can be taxed at the second piece of $12\%$
We have to move on to the third piece.
Third Piece for $\$p - 38700.00$The remaining income,$(p - 38700)$is taxed at$22\%$So, we have to multiply the remaining income by$0.22t(p) = 952.5 + 3501 + 0.22(p - 38700)t(p) = 952.5 + 3501 + 0.22p - 8514t(p) = 0.22p - 4060.5$For the fourth piece; We have to "finish" with the first, second, and third pieces First Piece for$\$9525.00$
tax for $\$9525$income @$10\%$per$\$$earned = 9525 * 0.1 = 952.5 Then, we move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. Please review the scenario in the Manual/Arithmetic Method 38700.00 - 9525.00 = 29175.00 \29175.00 is taxed at 12\% Second Piece for \29175.00 tax for \29175.00 income @ 12\% per \$$ earned = $29175.00 * 0.12 = 3501.00$
We are done with the maximum taxable income that can be taxed at the second piece of $12\%$
We move to the third piece.
We need to calculate the range of taxable income that should be taxed at the third tax rate.
$82500.00 - 38700.00 = 43800.00$
$\$43800.00$is taxed at$22\%$Third Piece for$\$43800.00$
tax for $\$43800.00$income @$22\%$per$\$$earned = 43800.00 * 0.22 = 9636.00 We are done with the maximum taxable income that can be taxed at the second piece of 22\% We move to the fourth piece. Fourth Piece for \p - 82500.00 The remaining income, (p - 82500) is taxed at 24\% So, we have to multiply the remaining income by 0.24 t(p) = 952.5 + 3501 + + 9636 + 0.24(p - 82500) t(p) = 952.5 + 3501 + 9636 + 0.24p - 19800 t(p) = 0.24p - 5710.5 For the fifth piece; We have to "finish" with the first, second, third, and fourth pieces First Piece for \9525.00 tax for \9525 income @ 10\% per \$$ earned = $9525 * 0.1 = 952.5$
Then, we move to the second piece.
We need to calculate the range of taxable income that should be taxed at the second tax rate.
Please review the scenario in the Manual/Arithmetic Method
$38700.00 - 9525.00 = 29175.00$
$\$29175.00$is taxed at$12\%$Second Piece for$\$29175.00$
tax for $\$29175.00$income @$12\%$per$\$$earned = 29175.00 * 0.12 = 3501.00 We are done with the maximum taxable income that can be taxed at the second piece of 12\% We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate. 82500.00 - 38700.00 = 43800.00 \43800.00 is taxed at 22\% Third Piece for \43800.00 tax for \43800.00 income @ 22\% per \$$ earned = $43800.00 * 0.22 = 9636.00$
We are done with the maximum taxable income that can be taxed at the third piece of $22\%$
We move to the fourth piece.
We need to calculate the range of taxable income that should be taxed at the fourth tax rate.
$157500.00 - 82500.00 = 75000.00$
$\$75000.00$is taxed at$24\%$Fourth Piece for$\$75000.00$
tax for $\$75000.00$income @$24\%$per$\$$earned = 75000.00 * 0.24 = 18000.00 We are done with the maximum taxable income that can be taxed at the fourth piece of 24\% We move to the fifth piece. Fifth Piece for \p - 157500.00 The remaining income, (p - 157500) is taxed at 32\% So, we have to multiply the remaining income by 0.32 t(p) = 952.5 + 3501 + + 9636 + 18000 + 0.32(p - 157500) t(p) = 952.5 + 3501 + 9636 + 18000 + 0.32p - 50400 t(p) = 0.32p - 18310.5 For the sixth piece; We have to "finish" with the first, second, third, fourth, and fifth pieces First Piece for \9525.00 tax for \9525 income @ 10\% per \$$ earned = $9525 * 0.1 = 952.5$
Then, we move to the second piece.
We need to calculate the range of taxable income that should be taxed at the second tax rate.
Please review the scenario in the Manual/Arithmetic Method
$38700.00 - 9525.00 = 29175.00$
$\$29175.00$is taxed at$12\%$Second Piece for$\$29175.00$
tax for $\$29175.00$income @$12\%$per$\$$earned = 29175.00 * 0.12 = 3501.00 We are done with the maximum taxable income that can be taxed at the second piece of 12\% We move to the third piece. We need to calculate the range of taxable income that should be taxed at the third tax rate. 82500.00 - 38700.00 = 43800.00 \43800.00 is taxed at 22\% Third Piece for \43800.00 tax for \43800.00 income @ 22\% per \$$ earned = $43800.00 * 0.22 = 9636.00$
We are done with the maximum taxable income that can be taxed at the third piece of $22\%$
We move to the fourth piece.
We need to calculate the range of taxable income that should be taxed at the fourth tax rate.
$157500.00 - 82500.00 = 75000.00$
$\$75000.00$is taxed at$24\%$Fourth Piece for$\$75000.00$
tax for $\$75000.00$income @$24\%$per$\$$earned = 75000.00 * 0.24 = 18000.00 We are done with the maximum taxable income that can be taxed at the fourth piece of 24\% We move to the fifth piece. We need to calculate the range of taxable income that should be taxed at the fifth tax rate. 200000.00 - 157500.00 = 42500.00 \42500.00 is taxed at 32\% Fifth Piece for \42500.00 tax for \42500.00 income @ 32\% per \$$ earned = $42500.00 * 0.32 = 13600.00$
We are done with the maximum taxable income that can be taxed at the fifth piece of $32\%$
We move to the sixth piece.
Sixth Piece for $\$p - 200000.00$The remaining income,$(p - 200000)$is taxed at$35\%$So, we have to multiply the remaining income by$0.35t(p) = 952.5 + 3501 + + 9636 + 18000 + 13600 + 0.35(p - 200000)t(p) = 952.5 + 3501 + 9636 + 18000 + 13600 + 0.35p - 70000t(p) = 0.35p - 24310.5$For the seventh piece; We have to "finish" with the previous six pieces in order First Piece for$\$9525.00$
tax for $\$9525$income @$10\%$per$\$$earned = 9525 * 0.1 = 952.5 Then, we move to the second piece. We need to calculate the range of taxable income that should be taxed at the second tax rate. Please review the scenario in the Manual/Arithmetic Method 38700.00 - 9525.00 = 29175.00 \29175.00 is taxed at 12\% Second Piece for \29175.00 tax for \29175.00 income @ 12\% per \$$ earned = $29175.00 * 0.12 = 3501.00$
We are done with the maximum taxable income that can be taxed at the second piece of $12\%$
We move to the third piece.
We need to calculate the range of taxable income that should be taxed at the third tax rate.
$82500.00 - 38700.00 = 43800.00$
$\$43800.00$is taxed at$22\%$Third Piece for$\$43800.00$
tax for $\$43800.00$income @$22\%$per$\$$earned = 43800.00 * 0.22 = 9636.00 We are done with the maximum taxable income that can be taxed at the third piece of 22\% We move to the fourth piece. We need to calculate the range of taxable income that should be taxed at the fourth tax rate. 157500.00 - 82500.00 = 75000.00 \75000.00 is taxed at 24\% Fourth Piece for \75000.00 tax for \75000.00 income @ 24\% per \$$ earned = $75000.00 * 0.24 = 18000.00$
We are done with the maximum taxable income that can be taxed at the fourth piece of $24\%$
We move to the fifth piece.
We need to calculate the range of taxable income that should be taxed at the fifth tax rate.
$200000.00 - 157500.00 = 42500.00$
$\$42500.00$is taxed at$32\%$Fifth Piece for$\$42500.00$
tax for $\$42500.00$income @$32\%$per$\$$earned = 42500.00 * 0.32 = 13600.00 We are done with the maximum taxable income that can be taxed at the fifth piece of 32\% We move to the sixth piece. We need to calculate the range of taxable income that should be taxed at the sixth tax rate. 500000.00 - 200000.00 = 300000.00 \300000.00 is taxed at 35\% Sixth Piece for \300000.00 tax for \300000.00 income @ 35\% per \$$ earned = $300000.00 * 0.35 = 105000.00$
We are done with the maximum taxable income that can be taxed at the sixth piece of $35\%$
We move to the seventh piece.
Seventh Piece for $\$p - 500000.00$The remaining income,$(p - 500000)$is taxed at$37\%$So, we have to multiply the remaining income by$0.37t(p) = 952.5 + 3501 + + 9636 + 18000 + 13600 + 105000 + 0.37(p - 500000)t(p) = 952.5 + 3501 + 9636 + 18000 + 13600 + 105000 + 0.37p - 185000t(p) = 0.37p - 34310.5$We can now write the piecewise function as: $$t(p) = \begin{cases} \\[3ex] 0.1p; & \quad 0 \leq p \leq 9525 \\[3ex] 0.12p - 190.5; & \quad 9525 \lt p \leq 38700 \\[3ex] 0.22p - 4060.5; & \quad 38700 \lt p \leq 82500 \\[3ex] 0.24p - 5710.5; & \quad 82500 \lt p \leq 157500 \\[3ex] 0.32p - 18310.5; & \quad 157500 \lt p \leq 200000 \\[3ex] 0.35p - 24310.5; & \quad 200000 \lt p \leq 500000 \\[3ex] 0.37p - 34310.5; & \quad p \gt 500000 \end{cases}$$ Let us recalculate all the questions using the Piecewise Function method. (1.)$\$7,000.00$ falls in the first piece.

$t(p) = 0.1p \\[3ex] t(7000) = 0.1(7000) \\[3ex] = 700 \\[3ex]$ tax for taxable income of $\$7,000.00$=$\$700.00$

(2.) $\$12,575.00$falls in the second piece.$ t(p) = 0.12p - 190.5 \\[3ex] t(12575) = 0.12(12575) - 190.5 \\[3ex] = 1509 - 190.5 \\[3ex] = 1318.5 \\[3ex] $tax for taxable income of$\$12,575.00$ = $\$1,318.50$(3.)$\$43,750.00$ falls in the third piece.

$t(p) = 0.22p - 4060.5 \\[3ex] t(43750) = 0.22(43750) - 4060.5 \\[3ex] = 9625 - 4060.5 \\[3ex] = 5564.5 \\[3ex]$ tax for taxable income of $\$43,750.00$=$\$5,564.50$

(4.) $\$120,327.00$falls in the fourth piece.$ t(p) = 0.24p - 5710.5 \\[3ex] t(120327) = 0.24(120327) - 5710.5 \\[3ex] = 28878.48 - 5710.5 \\[3ex] = 23167.98 \\[3ex] $tax for taxable income of$\$120,327.00$ = $\$23,167.98$(5.)$\$165,428.00$ falls in the fifth piece.

$t(p) = 0.32p - 18310.5 \\[3ex] t(165428) = 0.32(165428) - 18310.5 \\[3ex] = 52936.96 - 18310.5 \\[3ex] = 34626.46 \\[3ex]$ tax for taxable income of $\$165,428.00$=$\$34,626.46$

(6.) $\$234,543.00$falls in the sixth piece.$ t(p) = 0.35p - 24310.5 \\[3ex] t(234543) = 0.35(234543) - 24310.5 \\[3ex] = 82090.05 - 24310.5 \\[3ex] = 57779.55 \\[3ex] $tax for taxable income of$\$234,543.00$ = $\$57,779.55$(7.)$\$700,712.00$ falls in the seventh piece.

$t(p) = 0.37p - 34310.5 \\[3ex] t(700712) = 0.37(700712) - 34310.5 \\[3ex] = 259263.44 - 34310.5 \\[3ex] = 224952.94 \\[3ex]$ tax for taxable income of $\$700,712.00$=$\$224,952.94$

Ask students their preferred method - solving it manually or solving it by piecewise function.
They should give reasons for their answers.
Ask students if any of them can come up with another method besides the two methods already discussed.

Before we develop the calculator for the 2018 Federal Income Tax, we need to write the Piecewise Functions for the other filing options.
We can ask the user to select any of the filing options to calculate the tax.
If you follow the example for the Single filing option, you should get the same results that I get.
Please verify your results with my own. If you find any discrepancy even by one cent, please let me know.

The Piecewise Function for the Head of Household is: $$t(p) = \begin{cases} \\[3ex] 0.1p; & \quad 0 \leq p \leq 13600 \\[3ex] 0.12p - 272; & \quad 13600 \lt p \leq 51800 \\[3ex] 0.22p - 5452; & \quad 51800 \lt p \leq 82500 \\[3ex] 0.24p - 7102; & \quad 82500 \lt p \leq 157500 \\[3ex] 0.32p - 19702; & \quad 157500 \lt p \leq 200000 \\[3ex] 0.35p - 25702; & \quad 200000 \lt p \leq 500000 \\[3ex] 0.37p - 35702; & \quad p \gt 500000 \end{cases}$$

The Piecewise Function for the Married Filing Jointly or Qualifying Widow is: $$t(p) = \begin{cases} \\[3ex] 0.1p; & \quad 0 \leq p \leq 19050 \\[3ex] 0.12p - 381; & \quad 19050 \lt p \leq 77400 \\[3ex] 0.22p - 8121; & \quad 77400 \lt p \leq 165000 \\[3ex] 0.24p - 11421; & \quad 165000 \lt p \leq 315000 \\[3ex] 0.32p - 36621; & \quad 315000 \lt p \leq 400000 \\[3ex] 0.35p - 48621; & \quad 400000 \lt p \leq 600000 \\[3ex] 0.37p - 60621; & \quad p \gt 600000 \end{cases}$$

The Piecewise Function for the Married Filing Separately is: $$t(p) = \begin{cases} \\[3ex] 0.1p; & \quad 0 \leq p \leq 9525 \\[3ex] 0.12p - 190.5; & \quad 9525 \lt p \leq 38700 \\[3ex] 0.22p - 4060.5; & \quad 38700 \lt p \leq 82500 \\[3ex] 0.24p - 5710.5; & \quad 82500 \lt p \leq 157000 \\[3ex] 0.32p - 18270.5; & \quad 157000 \lt p \leq 200000 \\[3ex] 0.35p - 24270.5; & \quad 200000 \lt p \leq 300000 \\[3ex] 0.37p - 30270.5; & \quad p \gt 300000 \end{cases}$$

Which of the two methods do you prefer?
What are your reasons?
What are the pros and cons that you see for each method?
Do you have any other method for solving Piecewise Function applications?

Yearly Tax Statement for $2018$

Please test the calculator and see the output.
Complete all fields. Then, click "Tax Statement".

• Taxable Income

• $2018$ Tax Statement

Income Taxes

Please review the calculations and test the calculator first.
You may only do the income taxes of any of the filing options for the current year or future year(s).
If you do the income taxes of the filing options for the current year, it should be before the first IRS deadline for filing taxes. If the IRS deadline is past, then you have to do for future years.
You may NOT do the income taxes of any of the filing options of any previous year(s).

For Mathematics and Information Technology/Computer Science Students: Midterm Project

(1.) You may work as a group (peer tutor to teach and correct one another).
However, this is an individual project.
In other words, you will submit your own project.

(2.) No two projects should be the same.

(3.) Please write the direct website of the company/organization where you got the tax information.
If you wish to work on $2020$ tax rates, this website is okay: IRS.com (This is NOT IRS.gov)
Please note that it is your responsibity to ensure that the tax information is correct.
In that regard, please compare your information with the information across several reputable websites.
Please work only on Federal Taxes. Please do not work on State, City, or County taxes.
For any filing option you do, please cover all the pieces.
You may file:
(A.) Single OR
(B.) Head of Household OR
(C.) Married Filing Jointly or Qualifying Widow OR
(D.) Married Filing Separately

(4.) Write the complete address of the direct page of the website where you found the application.
(a.) *If the "direct" web address is too long, please shorten it by pasting the "complete web address" into www.tinyurl.com
* *This is only for traditional students (onsite) students*
*Generate a short address and write that address "as is".*
(b.) For online students, please copy and paste the link "as is".
(c.) Please set the link to open in a new window.

(5.) I understand some of you do not want to type directly in the Blackboard editor using the Math Editor.
You may:
(a.) Show all your work on paper, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor. OR
(b.) Show all your work in Microsoft Word, write all math terms appropriately, take clear screenshots of your entire work, and insert those screenshots as images directly on the Blackboard editor.
Please DO NOT submit any attachment on Blackboard. It will not be clicked. It will not be opened. It will not be graded.

(6.) If you need feedback on your project before submission, please submit your project as a draft in the Project Drafts forum on Blackboard.
You may also send it to me as an attachment via email. I shall review and provide feedback.
Draft projects are to be submitted in the Project Drafts forum. Draft projects are not graded.
Actual projects that needs to be graded should be submittied in the actual Project forum.

(7.) Research Skills: Cite your source properly. Use APA, MLA, or Chicago Manual of Style. Indicate the style you used.

(8.) Writing Skills: Write or type the "main" application entirely.

(9.) Mathematical Skills: Arithmetic Use random numbers to test the real-world application manually for each piece.
Write down your results.

(10.) Mathematical Skills: Algebra: Write a piecewise function for that application.
Test the piecewise function with the same random numbers.
The results should be the same. If the results are not the same, fix it.

 Name: Your name Date: The date Instructor: Samuel Chukwuemeka Project: Federal Tax Rates, Brackets, and Standard Deductions Company: Bankrate.com or IRS.com or or any other website you used (https://www.bankrate.com/taxes/tax-brackets/) Objectives: (1.) Calculate the federal income taxes of any United States resident/citizen within each taxable income bracket manually using Arithmetic method. (2.) Write a piecewise function of the federal income tax rates. (3.) Recalculate the same income tax of the United States resident/citizen for those income brackets algebraically using the Piecewise Function method. Information: Write the direct information from the direct website Arithmetic Method: Test each piece manually Piecewise Function: Write the piecewise function of the information Piecewise Function Method: Test the same each piece algebraically Citation: Indicate the type of citation format. Cite your source accordingly.

Student Sample (Math Part):
(1.) Include the objective(s)
(2.) Include page numbers.
(3.) You need to do at least one filing option (one or more).
Angel is a diligent student who decided to do all filing options.
I am impressed with his work: both the Math Part (document) and the Programming Part (the website app: link is in the document)

The teacher should guide each student to the successful completion of the project.
Let students know you are willing to help.

For Information Technology/Computer Science Students: Midterm Project

Minimum Requirements for Beginning C++

These are the minimum requirements.
I understand I did all the four filing options for the $2018$ Federal Income Tax.
However, you are only required to do a minimum of one option.
You may choose to do all options if you prefer.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a console application.

(3.) The Input/Output feature should be used.

Error Handling
(4.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(5.) Make sure your executable file runs by itself outside the project folder
If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
You may also upload them directly if you prefer.
I shall review and provide feedback.
If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project.
When you submit it, I shall review and provide feedback.

If it does not run, then you need to fix it.
If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you.

(6.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course.

This is the reason:
Please review the Students section: Samples of Students Work
You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students.
FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students).
However, I will include your first name on my website if I use your work.

Minimum Requirements for Beginning VB.NET, Beginning C#, Beginning Java

These are the minimum requirements.
I understand I did all the four filing options for the $2018$ Federal Income Tax.
However, you are only required to do a minimum of one option.
You may choose to do all options if you prefer.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a desktop application.

(3.) Set the MinimumBox property of the form to True
We want to accommodate users with laptop/desktop smaller screen sizes too.
They should have the ability to adjust your application to fit their screen sizes.

(4.) The Input/Output feature should be used.

Error Handling
(5.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(6.) Make sure your executable file runs by itself outside the project folder
If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
You may also upload them directly if you prefer.
I shall review and provide feedback.
If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project.
When you submit it, I shall review and provide feedback.

If it does not run, then you need to fix it.
If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you.

(7.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course.

This is the reason:
Please review the Students section: Samples of Students Work
You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students.
FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students).
However, I will include your first name on my website if I use your work.

Minimum Requirements for Advanced C++

These are the minimum requirements. Please be creative.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a console application.

(3.) Input/Output feature should be used.

(4.) Class should be used.

(5.) Constructor(s) should be used.

(6.) Property/Properties should be used.
The class member: Taxable Income should be private.

(7.) Method(s) should be used.

Error Handling
(8.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(9.) Make sure your executable file runs by itself outside the project folder
If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
You may also upload them directly if you prefer.
I shall review and provide feedback.
If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project.
When you submit it, I shall review and provide feedback.

If it does not run, then you need to fix it.
If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you.

(10.) When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course.

This is the reason:
Please review the Students section: Samples of Students Work
You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students.
FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students).
However, I will include your first name on my website if I use your work.

These are the minimum requirements. Please be creative.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a desktop application.

(3.) Set the MinimumBox property of the form to True
We want to accommodate users with laptop/desktop smaller screen sizes too.
They should have the ability to adjust your application to fit their screen sizes.

(4.) Input/Output feature should be used.

(5.) Class should be used.

(6.) Constructor(s) should be used.

(7.) Property/Properties should be used.
The class member: Taxable Income should be private.

(8.) Method(s) should be used.

Error Handling
(9.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(10.) Make sure your executable file runs by itself outside the project folder
If it does run, include all these: (documentation of all your Math work and the .exe file) in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
You may also upload them directly if you prefer.
I shall review and provide feedback.
If your submission works well, I shall ask you to submit the Project folder. The Project folder is the folder that is created when you create a new project.
When you submit it, I shall review and provide feedback.

If it does not run, then you need to fix it.
If you cannot fix it and you have reviewed the resources, please attend the Office Hours/Live Sessions so I can help you.

When you are done (everything works well), please zip the entire project: (documentation of the Math, executable file that runs by itself outside the Project folder, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course.

This is the reason:
Please review the Students section: Samples of Students Work
You can run any of those files (no worries, the files are safe) and you will see the work of some of my previous students.
FERPA (Federal Educational Rights and Privacy Act) law would not allow me to ask you to include your first and last name (even though you are doing the project) because I will include some of the executable files on my website for my students (just as you saw the works of my previous students).
However, I will include your first name on my website if I use your work.

Minimum Requirements for ASP.NET

These are the minimum requirements. Please be creative.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a web application.
You may use Functional Programming or Object-oriented Programming.
You may use ASP.NET Web Forms, ASP.NET Web Pages, ASP.NET MVC, or any other ASP.NET web platform.
You may use C# or VB.NET

(3.) The Input/Output feature should be used.
Use nice HTML elements and CSS.
Functionality is the most important factor.
However, aesthetics and user-friendliness are also important factors in Web Design.

Error Handling
(4.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(5.) Include the URL of the web application (web address) in the documentation of your Math work.
Please make sure the web application is accessible.
The draft project should contain: documentation of Math work, the web application address, and the Project folder.
The Project folder is the folder that is created when you create a new project. It contains all folders and files.
Include all these in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
I shall review and provide feedback.

(6.) When you are done (everything works well), please zip the entire project: (documentation of the Math that includes the URL, and the Project folder) into one folder; and submit the zipped folder (.zip only) in the actual Midterm Project forum of the Blackboard course.

Minimum Requirements for JavaScript

These are the minimum requirements. Please be creative.

(1.) Please use appropriate naming for your project application.
The application should display at least the same output of my calculator.
That implies that you should test my calculator to see the output.

(2.) The application should be a web application.

(3.) The Input/Output feature should be used.
Use nice HTML elements and CSS.
Functionality is the most important factor.
However, aesthetics and user-friendliness are also important factors in Web Design.

Error Handling
(4.) Alert the user/Display an appropriate error message to the user, if the taxable income is negative.

(5.) Include the URL of the web application (web address) in the documentation of your Math work.
Please make sure the web application is accessible.
Ensure that you follow the best practices: link to the external CSS file in the head element and the link to the external JS file right before the closing body element.
The draft project should contain: documentation of Math work that includes the URL.
Include the draft project in OneDrive, create a shareable link, and post the link in the Midterm Project Drafts forum of the course on Blackboard or send to me via email.
I shall review and provide feedback.

(6.) When you are done (everything works well), please submit the entire project: (documentation of the Math that includes the URL) in the actual Midterm Project forum of the Blackboard course.

Optional

Further Work
Writing Skills: Submit a Reflection Journal.
Include your challenges, and how you overcame those challenges.
Technology Skills:
Include penalties for late payments in your project.
Write a mobile application for the project.
Develop a mobile application that sends reminders to residents/citizens to file their taxes on time.

Graphing Piecewise Functions

To graph a piecewise function:

(1.) Write the Table of Values for each piece

(2.) Make sure the end points for the domain of each piece are indicated in each Table of Value

(3.) Specify whether each end point is defined or undefined.

(4.) Plot each Table of Values on a graph.
Any end point that is defined should be labeled as a closed circle. This means that the end point is included in the domain for that piece.
Any end point that is not defined should be labeled as an open circle. This means that the end point is not included in the domain for that piece.

Let us do an example.

Example 1: ACT Which of the following is the graph of the function f(x) defined below?

$f(x) = \begin{cases} x^2 - 2 \enspace \text{for} \enspace x \le 1 \\[3ex] x - 7 \enspace \text{for} \enspace 1 \lt x \lt 5 \\[3ex] 4 - x \enspace \text{for} \enspace x \ge 5 \end{cases} \\[7ex]$

Let us draw the Table of Values for each function/piece
Then, we shall answer the question by going through each option and eliminating the incorrect options until we find the correct one

 $x$ $-2$ $-1$ $0$ $1$ $y$ $2$ $-1$ $-2$ $-1$ defined

 $x$ $1$ $2$ $3$ $4$ $5$ $y$ $-6$ $-5$ $-4$ $-3$ $-2$ undefined undefined

 $x$ $5$ $6$ $7$ $8$ $y$ $-1$ $1$ $2$ $3$ defined

Option F.
First Piece: when $x = 1$, $y = -3$
This is incorrect...as seen from the Table.

Option J.
First Piece: when $x = 1$, $y = 0$
This is incorrect...as seen from the Table.

Option G.
First Piece: when $x = -2$, $y = 0$
This is incorrect...as seen from the Table.

Option K.
This is the correct option because all the Tables of Values corresponds to the graph
This includes where the values are defined (closed circles) and undefined (open circles)
You may STOP here (or if you have time, check the last option)

Option H.
First Piece: when $x = 0$, $y = 0$
This is incorrect...as seen from the Table.

We can sketch the graph:
(1.) Manually on a graph paper
(2.) Using a graphing calculator/technology.

Let us sketch the graph using the TI-84 Plus Graphing Calculator
Step 1:

Step 2:
Enter the function and the domain of each piece
Enclose the function in parenthesis
Enclose the domain in parenthesis
Let us begin with the first piece

Step 3:

Step 4:

Step 5:
Graph the piecewise function

Greatest Integer Function

The greatest integer function is also called the floor function.

The greatest integer of a number is defined as the greatest integer less than or equal to that number.

The greatest integer of a number, say $x$ is denoted by ${\lfloor x \rfloor}$ or $[\![ x ]\!]$

$\mathbb{Z}$ is the set of all integers.

Say we have a decimal: $\large x.y$;
$x$ is the integer part.

{\lfloor x \rfloor} = \left \{\begin{aligned} & x; && x \: \epsilon \: \mathbb{Z} \\[2ex] & x; && x.y > 0 \\[2ex] & x-1; && x.y < 0 \end{aligned} \right.

Greatest Integer Function Calculator

The greatest integer of $\:$ =

Least Integer Function

The least integer function is also called the ceiling function.

The least integer of a number is defined as the least integer greater than or equal to that number.

The least integer of a number, say $x$ is denoted by ${\lceil x \rceil}$ or $]\!]x[\![$

$\mathbb{Z}$ is the set of all integers.

Say we have a decimal: $\large x.y$;
$x$ is the integer part.

$${\lceil x \rceil} = \begin{cases} x, & \quad \text{if }\: x \: \epsilon \: \mathbb{Z} \\[2ex] x + 1, & \quad \text{if }\: x.y > 0 \\[2ex] x, & \quad \text{if }\: x.y < 0 \end{cases}$$

Did you notice we wrote this piecewise function in another way? It is still acceptable this way.

Least Integer Function Calculator

The least integer of $\:$ =

Absolute Value Function

The absolute value function is sometimes called the modulus function. (not modulo function)

The absolute value of a number is defined as the magnitude of the number regardless of sign.

This implies that the absolute value of a number must either be zero, or positive.

The number can be negative, zero, or positive.

However, the absolute value cannot be negative.

It can either be zero (if the number is zero), or positive (if the number is negative or positive).

The absolute value of a number, say $x$ is denoted by $|x|$

$$|x| = \begin{cases} -x; & \quad x< 0 \\[2ex] x; & \quad x≥ 0 \end{cases}$$

Absolute Value Function Calculator

The absolute value of $\:$ =

References

Chukwuemeka, S.D (2016, April 30). Samuel Chukwuemeka Tutorials - Math, Science, and Technology. Retrieved from https://www.samuelchukwuemeka.com

2020 Federal Tax Rates, Brackets, & Standard Deductions. (2020, January 25). IRS.Com. https://www.irs.com/articles/2020-federal-tax-rates-brackets-standard-deductions/

Bankrate.com. (2018, November 28). 2018-2019 Tax Brackets | Bankrate.com. Retrieved from https://www.bankrate.com/finance/taxes/tax-brackets.aspx

Calhoun County Water Association. (n.d.). Calhoun County Water Association. Retrieved from http://www.calhouncwa.com/rates.htm

Georgia Public Service Commission. (n.d.). Georgia Public Service Commission. Retrieved from http://www.psc.state.ga.us/calc/electric/GPcalc.asp

Kelly Phillips Erb. (2019, January 30). New: IRS Announces 2018 Tax Rates, Standard Deductions, Exemption Amounts And More. Retrieved from https://www.forbes.com/sites/kellyphillipserb/2018/03/07/new-irs-announces-2018-tax-rates-standard-deductions-exemption-amounts-and-more/#3c6ec333133d