Piecewise Defined Functions

Lesson 2.3

How to Write a Weird Function

• What if we had to write a single function to describe this graph …

• We must learn how to specify different formulas for different parts of the domain

Absolute Value Function

• Whatever you put into the functioncomes out positive

-3

+3

+7

+7

Absolute Value Function

• Definition

0

0)(

xifx

xifxxabsx

Use the abs( ) function on your calculator

Use the abs( ) function on your calculator

Absolute Value Function

• Note the graph of y = | x |

• Table of values

Piecewise Defined Functions

• Consider a function defined differently for different parts of the domain (the x values)

• Consider what the table of values looks like

2 for x x

2 x 0for 2)( 2

xxf

Piecewise Defined Functions

2 for x x

2for x 2)( 2

xxfx y

-1

0

1

2

3

4

Piecewise Defined Functions

• Our calculatorhandles piecewisefunctions with thewhen ( ) command

2 for x x

2for x 2)( 2

xxf

What will the graph look like?

What will the graph look like?Use Diamond 0 for

the ≤ sign

Use Diamond 0 for the ≤ sign

Piecewise Defined Functions

Piecewise Defined Functions

• Condition

• Expression to usewhen conditionis true

• Expression to use when condition is false

Piecewise Defined Functions

• Try entering and graphing the following function

2 for x 4

2 for x x - 4)(xg

Piecewise Defined Functions

Assignment

• Lesson 2.3

• Page 76

• Exercises 1, 3, 5, 7, 9, 11, 13, 15, 17,