Collins Type 2(Turned in)

• Describe when and why you would use the vertical-line test and the horizontal-line test.

SATProblem of the Day

2.6.1 Special Functions2.6.1 Special Functions2.6.1 Special Functions2.6.1 Special FunctionsObjectives: •Write, graph, and apply piecewise functions

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

Example 1Graph the following function:

3x if 0 x 2

f(x) 6 if 2 x 4

x 10 if 4 x 6

1

21 3 4 5

2

3

5

4

6

6

x y

066

022

6464

46

Example 2Graph the following function:

x 2 if x 2

f(x) 4 if 2 x 2

x 2 if 2 x

PracticeGraph the following function:

2x 3 if 0 x 5f(x)

3x 8 if 5 x 10

PracticeWrite the equations for the function shown.

Example 3Write the equations for the function shown.

Homework

Read Lesson 2.6 in Textbook

Do Exercises 17-27 Odd

Warm-UpGraph the piecewise function:

4 minutes

x 5 if x 5

f(x) 2 if 5 x 5

x 5 if 5 x

2.6.2 Special Functions2.6.2 Special Functions2.6.2 Special Functions2.6.2 Special FunctionsObjectives: •Write, graph, and apply step and absolute-value functions

Step FunctionsA step function is a piecewise function that consists of different constant range values for different intervals of the domain of the function.

1

-2-3 -1-1

2

-3

-2

3

1 3

2

Rounding-down function

1

-2-3 -1-1

2

-3

-2

3

1 3

2

Rounding-up function

Greatest integer function

f (x) x , or f(x) x f (x) x

Example 1Graph the following function:

f (x) 2 x

PracticeGraph the step function:

g(x) x 1

Absolute-Value Functions

x x if x 0f(x)

x x if x 0

The absolute-value function, denoted by

can be defined as a piecewise function as follows:

f (x) x ,

Example 1Graph the following function:

f (x) 3 x 2

PracticeGraph the following function:

f (x) x 2

PracticeGraph the following function:

1g(x) x 1

2

Collins Type 2

Is the inverse of y = |x| a function? Explain.

Homework

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