Review of step and piecewise functions
Graph the following step functions:
3

1. f (x )  1
 1

0 x3
if
3 x 6
6 x9
8

2. f (x)  5
 2

2 x4
if
0 x2
2 x  0
3. The charge to rent a jet ski is $5.00 for the first hour and $2.00 for each additional hour
or fraction thereof. The fee is a function of the time the jet ski is used.
a) Sketch the graph of a step function that models this cost.
b) Write an equation for the linear function that approximates the cost. Sketch the
graph of this linear function.
4. Graph the following piecewise functions:
a)
5 x  1
x2
if
f ( x)  
x2
x  9
x  1

c) f ( x)   x 2
if
 x  2

x  2
2  x 1
x 1
4
x  2
 2
b) f ( x )   x if  2  x  2
4
x2

x  1
3

d) f ( x )   2 x  1 if  1  x  2
5
x2

5. Arnold is working in a job that pays him $8/hr, if he works for 40 hours or less for a
week. He gets 1.5 times his hourly rate for the hours he works beyond 40 hours.
a) Write and Graph the piecewise function that will give the weekly pay ‘p’ in terms of
the number of hours ‘h’ he works.
b) What is the amount he will get if he works for 42 hours?
6. Write the Equations for the following piecewise functions.
a)
c)
7.
b)
d)