“Roads? Where we’re going, we don’t need roads.”
2.5 Library of Functions and Piece-Wise
Functions
Piece-Wise Functions
x 2
x 0

f (x)  2 0  x  2
 x
x 2

Domain:
y-int:
x-int:
5
Find the following:
4
1) f (2)
3
2
1
2) f (1)
-5 -4 -3 -2 -1
1
-1
3) f (4)
-2
-3
-4
-5
2
3
4
5
Piece-Wise Functions
x  2 3  x  1

f (x)   x
1 x  4
 x  4
x4

Domain:
y-int:
x-int:
5
Find the following:
4
1) f (2)
3
2
1
2) f (4)
-5 -4 -3 -2 -1
1
-1
3) f (6)
-2
-3
-4
-5
2
3
4
5
Piece-Wise Functions
Find the domain, intercepts, and graph each function.
3,  4  x  0

f ( x)   0, x  0
 3, 0  x  4

1, 0  x  4
f ( x)  
 x  5, x  0
D:
D:
y-int:
x-int:
y-int:
x-int:
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
2
3
4
5
Piece-Wise Functions
Write a rule for a piece-wise function for each graph.
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
2
3
4
5
Piece-Wise Application
The function below represents the monthly cost C for x minutes
of cell phone usage.

0  x  600
 50,
C(x)  2
x 190,
x  600

5
1) How much is the monthly charge for 425 minutes of usage?
600 minutes? 710 minutes?

2) How many minutes were used in one month if the cost was
$167.00?
2.5 Library of Functions and Piece-Wise
Functions
Homework #24: p.115
#25, 29 – 37 odd
#41, 43
Roads? Where we’re going we don’t need roads.