Sullivan Algebra & Trigonometry: Section 3.4

Library of Functions;Piecewise-Defined Functions

Objectives

• Graph the Functions in the Library of Functions

• Graph Piecewise-defined Functions

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.

The Constant Functioncxf )( x

y (0,c)

The Identity Function

xxf )(x

y

(0,0)

The Square Function

x

y

(0,0)

The Cube Function

2)( xxf

3)( xxf x

y

(0,0)

The Square Root Function

x

y

(0,0)xxf )(

x

y

(1,1)

(-1,-1)

The Reciprocal Function

xxf

1)(

(0,0) x

yThe Absolute Value Function

xxf )(

The Cube Root Function

x

y

3)( xxf

When functions are defined by more than one equation, they are called piecewise- defined functions.

Example: The function f is defined as:

1 3

1 3

12- 3

)(

xx

x

xx

xf

a.) Find f (1) = 3Find f (-1) = (-1) + 3 = 2

Find f (4) = - (4) + 3 = -1

1 3

1 3

12- 3

)(

xx

x

xx

xf

b.) Determine the domain of f

Domain: in interval notation),2[

or in set builder notation}2|{ xx

c.) Graph f

x

y

1 2 3

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1

d.) Find the range of f from the graph found in part c.

Range: in interval notation)4,(

or in set builder notation}4|{ yy

x

y

1 2 3

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