The goals of this assignment/project are:

1. to write a piece wise function based on a real situation of a US state income tax

2. to graph the piece wise function you have written using Desmos and save it for posting on Blackboard.

3. to identify the range and domain in interval notation of the piece wise function

4. to determine the limits of the piece wise function that was graphed at the point the amount of tax changes due to a new income bracket

5. to communicate mathematically by writing and working collaborative with classmates to determine where the piece wise function is continuous or not and analyze to the continuity of the functions at various endpoints Based on your assigned state and filing status, answer the following questions.

Grading rubric is at the end of this document.

a. Write a piece wise function f(x) for the state you have been assigned to write the piece wise function.

b. Graph each one using Desmos.com. Save your graph so that you can upload it on Blackboard.

c. What is the domain of the function in interval notation?

d. What is the range of the function in interval notation?

e. What is the constant interval?

f. Are there any points of discontinuity? If so where are there located?

g. Where is the derivative of your graph equal to zero? Explain.

h. Is there a maximum value? If so, what is it? i. Is there a minimum value? If so, what is it?

j. What is the interval of decrease?

j. What is the interval of increase?

For earnings between $0.00 and $20,000.00, you'll pay 3%

For earnings between $20,000.00 and $100,000.00, you'll pay 5% plus $600.00

For earnings between $100,000.00 and $200,000.00, you'll pay 5.5% plus $4,600.00

For earnings between $200,000.00 and $400,000.00, you'll pay 6% plus $10,100.00

For earnings between $400,000.00 and $500,000.00, you'll pay 6.5% plus $22,100.00

For earnings between $500,000.00 and $1,000,000.00, you'll pay 6.9% plus $28,600.00

For earnings over $1,000,000.00, you'll pay 6.99% plus $63,100.00