1. 4 minutes
Warm-Up
Graph the function , and then use the horizontal-line test to determine if the inverse is a function.

2. Objectives: Write, graph, and apply piecewise functions
2.6.1 Special Functions
Objectives:
Write, graph, and apply piecewise functions

3. Piecewise Functions
A piecewise function consists of different function rules for different parts of the domain.

4. Example 1 Graph the following function: x y 2 6 2 6 4 6 4 6 6 4 1 2 35 6 2 6 2 6 4 6 4 6 6 4

5. Example 2
Graph the following function:

6. Practice
Graph the following function:

7. Example 3 Write the equations for the function shown.
(use SMART Board)

8. Practice
Write the equations for the function shown.
(use SMART Board)

9. Homework
p.129 #17-27 odds

10. 4 minutes
Warm-Up
Graph the piecewise function:

11. Objectives: Write, graph, and apply step and absolute-value functions
2.6.2 Special Functions
Objectives:
Write, graph, and apply step and absolute-value functions

12. Step Functions
A step function is a piecewise function that consists of different constant range values for different intervals of the domain of the function.
Greatest integer function
Rounding-down function
Rounding-up function 1 -2 -3 -1 2 3 1 -2 -3 -1 2 3

13. Example 1
Graph the following function:

14. Homework
p.130 #53,55

15. 4 minutes
Warm-Up
Graph the step function:

16. Objectives: Write, graph, and apply step and absolute-value functions
2.6.3 Special Functions
Objectives:
Write, graph, and apply step and absolute-value functions

17. Absolute-Value Functions
The absolute-value function, denoted by
can be defined as a piecewise function as follows:

18. Example 1
Graph the following function:

19. Practice
Graph the following function:

20. Practice
Graph the following function:

21. Homework
study guide