1. 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

2. Piecewise Functions
01
01
)(
2
xx
xx
xf
“Pieces of
the
Function”
Domain of
each piece
A single
function, f

3. Evaluating Piecewise
01
01
)(
2
xx
xx
xf
)2(f )0(f )4(f

4. Piecewise Functions
14
132
)(
xx
xx
xf

5. Absolute Value Function
xxf )(
Can also be expressed as:
0
0
)(
xx
xx
xf

6. Absolute Value Function
0
0
)(
xx
xx
xf
Domain?

7. Graphing Functions
Method 1: Plotting Points (T-Chart)
3)( xxg
Find the
domain of
the
function, bef
ore making
the T-Chart

8. Graphing Functions
Method 1: Plotting Points (T-Chart)
3)( xxg

9. Graphing Functions
Method 1: Plotting Points (T-Chart)
xxf 2)(

10. 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

11. Reading Graphs of Functions
(Similar to what we’ve already done)
1 2 3 4
1
2
3
4
)(xf
xxf ,3)(
xxf ,0)(

12. Positive / Negative Functions
1 2 3 4
1
2
3
4
)(xf
0)(xf
0)(xf

13. Positive/Negative Functions
Without 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

14. Positive/Negative Functions
Without a graph:
The Sign Test
0)(th
0)(th
824)( xth
Find Intervals Where:

15. Increasing / Decreasing Functions
1 2 3 4
1
2
3
4
)(xf
.)( incxf
.)( decxf

16. 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)

17. Determining if a graph is a function
The Vertical Line Test

18. Classwork
• Go over worksheet as class