2.5 Library of Functions and Piece-Wise
Functions
Aaron: Dude, one thing the guy said is you don’t taunt voodoo.
Zak: Am I taunting?
Aaron: Dude, you’re taunting the crap out of it!
Zak: I am sorry, I am not taunting you I am just talking…Talking loudly!
Library of Functions
1
1
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1
Linear Function
Square Function
Cube Function
Square Root Function
f ( x)  mx  b
f ( x)  x 2
f ( x)  x3
f ( x)  x
1
1
1
Cube Root
f ( x)  3 x
1
1
Reciprocal
1
f ( x) 
x
1
1
1
Absolute Value
Greatest Integer
f ( x)  x
f ( x)  x  int( x)
greatest integer less than or equal to x
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.
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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: p.115
#25 – 37 odd
#41, 43
Aaron: Dude, one thing the guy said is you don’t taunt voodoo.
Zak: Am I taunting?
Aaron: Dude, you’re taunting the crap out of it!
Zak: I am sorry, I am not taunting you I am just talking…Talking loudly!