Piecewise + Absolute Value Functions

Name: _________________________________________# ____ Period: __________ Date: ________________

1) Delmon has saved $600 and wants to open her first checking account. Which bank offers the lowest monthly charge?

Bank Monthly Charges

Central Bank $6 plus $.35 for each check you write

Main St. Bank $3 plus $.75 for each check you write

Co-op Bank $10, no matter how many checks you write

Create a graph to represent the best graph and highlight when it would be best to use each bank. (You can use a calculator to check, but I want to see the evidence on your graph)

What type of graph and function did you create when you highlighted the graph? Write the name of the function and how you would represent it below.

Give an example of someone (real or fictional) who might want to choose each of the banks above and why they would choose them.

2) Michelle Jacobson received job offers from two department stores, Clothing Galore and Fits You Right. Clothing Galore offered Michelle an 8% commission on all sales. Fits you Right offered her $1250 per month plus a 4% commission on all sales over $10,000.

a. Express Michelle’s possible monthly earnings at Clothing Galore as a function of her sales.

b. Express Michelle’s possible monthly earnings at Fits you Right as a function of her sales.

c. Write a piecewise function showing when it would be best to use each store.

d. Which job would you recommend that Michelle accept and why?

3) The graph below shows the monthly cost of Zachary’s long-distance calling plan as a function of the length of time her talks on the phone.

a. Write a piecewise function for the graph.

b. Zachery wants his monthly long distance phone bill to be no more than $20. Find the

maximum length of time he can call long distance.

4) Using an electronic device called a depth finder, the captain of a fishing boat measures the water depth to be 550 feet. Assume that the difference of the actual and measured depths is at most 5% of the actual depth.

a. The absolute difference between x and any fixed number a is given by the equation y=|x−a|. Write a function f(x) that gives the absolute difference of the actual depth x and the measure depth.

b. What is the domain and range of this function?

c. You write “5% of the actual depth x” as .05x. Graph the function from part (a) and f(x) = .05x on the same axes.

d. What are the intersection points? What do these values mean?

Graph each of the following (on the calculator if you prefer) and provide the domain, range, and write out the problem as a piecewise function.

Domain Range Piecewise Function1) y=¿

2) y=¿x−1∨¿

3) y=2∨x∨+3

4) y=2∨x+3∨¿

5) y=3|¿x−4|∨−2

6) y=−4∨x+2∨+1