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Warm-UpGraph the function , and then use the horizontal-line test to determine if the inverse is a function.
4 minutes
y x
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
Example 3Write the equations for the function shown.
(use SMART Board)
PracticeWrite the equations for the function shown.
(use SMART Board)
Homework
p.129 #17-27 odds
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
Homework
p.130 #53,55
Warm-UpGraph the step function:
4 minutes
g(x) x 1
2.6.3 Special Functions2.6.3 Special Functions2.6.3 Special Functions2.6.3 Special FunctionsObjectives: •Write, graph, and apply step and absolute-value functions
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) x 2
PracticeGraph the following function:
f (x) 3 x 2
PracticeGraph the following function:
1g(x) x 1
2
Homework
study guide
