Piecewise Functions
For each function, find f(-2), f(-1), f(0), f(1) and
f(2).
 x  1 if x  0
1) f ( x)  
 x  1 if x  0
if x  1
 3
2) f ( x)  
 2 x  5 if x  1
Graph the piecewise functions.
 x  1 if x  0
3) f ( x)  
 x  1 if x  0
9)
if x  1
 3
4) f ( x)  
 2 x  5 if x  1
 2 if x  2

5) f ( x)   1
 2 x if x  2
2 x  2 if x  1
6) f ( x)  
 x  1 if x  1
Write the piecewise function given the graph.
7)
8)
10)
11) A consultant charges $250 for the first four
hours of work. She then charges $50 per hour
after four hours. Write and graph an equation for
the function.
12) A movie theater ticket cost $5 for children
under 12 years old. The teenager (12-18 year
old) ticket cost $7 and adult cost $12. The senior
citizen tickets cost $9. Define and graph a
piecewise function.
21)
-5x +8(x - 2) = 5x - 22
22)
6 + 6x = 3x - x +14
23)
-5x -8(x +1) = -112
Solve the inequality.
13) A person is on a road trip. The car is
traveling $5 miles per hour for 2 hours. The car
then stops for 3 hours. The car continues
traveling at a rate of 15 miles per hours for 3
hours. Define and graph a piecewise function for
(y) miles and (x) time.
14) At Maston Lake you can rent a kayak for $20
for the first 4 hours. Time greater than 4 hours is
charged a rate of $5 an hour. Define and graph
the piecewise function.
15) At Sica Lake you can rent a kayak for $5 per
hour 3 hours. Time greater than 3 hours is
charged a rate of $10 an hour. Define and graph
the piecewise function.
Throw Back Problems:
Graph the equation.
2
x +1
3
17) f (x) = -3x - 2
16)
y=
18)
f (x) = ( x + 3) - 5
19)
y = - ( x - 2) + 4
2
2
20) y = x + 6x + 7
Solve the equation.
2
24)
-5(6x + 3) >165
25)
6x - 2(-8- 4x) ³ 86
26)
5 £ 8x - 7+ 4