Sullivan Algebra

1
Sullivan Algebra Trigonometry Section
3.4Library of FunctionsPiecewise-Defined
Functions

• Objectives
• Graph the Functions in the Library of Functions
• Graph Piecewise-defined Functions

2
The following library of functions will be used
throughout the text. Be able to recognize the
shape of each graph and associate that shape with
the given function.
y
(0,c)
The Constant Function
x
The Identity Function
3
The Square Function
The Cube Function
(0,0)
4
The Square Root Function
The Reciprocal Function
5
The Absolute Value Function
(0,0)
The Cube Root Function
6
When functions are defined by more than one
equation, they are called piecewise- defined
functions.
Example The function f is defined as
a.) Find f (1)
3
Find f (-1)
(-1) 3 2
Find f (4)
- (4) 3 -1
7
b.) Determine the domain of f
Domain in interval notation
or in set builder notation
c.) Graph f
8
d.) Find the range of f from the graph found in
part c.
Range in interval notation
or in set builder notation