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

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

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

Example 1 Graph the following function: x y 2 6 2 6 4 6 4 6 6 4 1 2 3 5 6 2 6 2 6 4 6 4 6 6 4

Example 2 Graph the following function:

Practice Graph the following function:

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

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

Homework p.129 #17-27 odds

4 minutes Warm-Up Graph the piecewise function:

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

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

Example 1 Graph the following function:

Homework p.130 #53,55

4 minutes Warm-Up Graph the step function:

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

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

Example 1 Graph the following function:

Practice Graph the following function:

Practice Graph the following function:

Homework study guide