Today’s Agenda

Attendance / Announcements◦ Need TI Graphing Calculator

◦ Exam 2 – Friday 10/11

Covers Chapters 3.1 to 3.7

Questions?

Sections 3.2

Piecewise Functions

01

01)(

2

xx

xxxf

“Pieces of the

Function”

Domain of each piece

A single function, f

Evaluating Piecewise

01

01)(

2

xx

xxxf

)2(f )0(f )4(f

Piecewise Functions

14

132)(

xx

xxxf

Absolute Value Function

xxf )(

Can also be expressed as:

0

0)(

xx

xxxf

Absolute Value Function

0

0)(

xx

xxxf

Domain?

Graphing FunctionsMethod 1: Plotting Points (T-Chart)

3)( xxg

Find the domain of

the function, before making the T-Chart

Graphing FunctionsMethod 1: Plotting Points (T-Chart)

3)( xxg

Graphing FunctionsMethod 1: Plotting Points (T-Chart)

xxf 2)(

Reading Graphs of Functions(Similar to what we’ve already done)

1 2 3 4

1

2

3

4

)( xf

)2(f

)1(f

)2(f

)4(f

Reading Graphs of Functions(Similar to what we’ve already done)

1 2 3 4

1

2

3

4

)( xf

xxf ,3)(

xxf ,0)(

Positive / Negative Functions

1 2 3 4

1

2

3

4

)( xf0)(xf

0)(xf

Positive/Negative FunctionsWithout a graph:

The Sign Test

Sign Test• Identify zero(s) of the function• Plot the zero(s) on a real number line• Choose a test point in each interval• Evaluate function at each test point

to determine the sign of f(x) on each interval

Positive/Negative FunctionsWithout a graph:

The Sign Test

0)(th

0)(th

824)( xth

Find Intervals Where:

Increasing / Decreasing Functions

1 2 3 4

1

2

3

4

)( xf

.)( incxf

.)( decxf

Graphing Functions

Determining if a graph is a function

The Vertical Line Test

This is a visual representation of what we did yesterday…Each input cannot have more than one output (not predictable)

Determining if a graph is a function

The Vertical Line Test

Classwork

• Go over worksheet as class