Functions Worksheet With Answer Key
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46Chapter Two
FUNCTIONS
Contents
2.1 Input and Output . . . . . . . . . . . . . .
70
Finding Output Values: Evaluating a Function
70
Evaluating a Function Using a Formula 70
Finding Input Values: Solving Equations . . .
71
Finding Output and Input Values From Tables
and Graphs . . . . . . . . . . . . .
72
2.2 Domain and Range . . . . . . . . . . . . .
78
Choosing Realistic Domains and Ranges . . .
79
Using a Graph to Find the Domain and Range
of a Function . . . . . . . . . . . .
79
Using Formulas and Graphs to Find Domains
and Ranges . . . . . . . . . . . . .
80
2.3 Piecewise-Defined Functions . . . . . . . . .
84
The Absolute Value Function . . . . . . . .
86
Visualizing Absolute Value on the
Number Line . . . . . . .
87
2.4 Preview of Transformations: Shifts . . . . .
90
Vertical Shift: The Heating Schedule for an
Office Building . . . . . . . . . . .
91
Horizontal Shift: The Heating Schedule . . .
92
Inside Versus Outside Changes . . . . . . .
93
Combining Horizontal and Vertical Shifts . .
94
2.5 Preview of Composite and Inverse Functions
97
Composition of Functions . . . . . . . . . .
97
Inverse Functions . . . . . . . . . . . . . .
99
Inverse Function Notation . . . . . .
99
Finding a Formula for the Inverse
Function . . . . . . . . . 100
Domain and Range of an Inverse
Function . . . . . . . . . 100
Relation Between Composition and Inverses:
A Function and Its Inverse Undo Each
Other
. . . . . . . . . . . . . . . 100
2.6 Concavity . . . . . . . . . . . . . . . . . . 104
Concavity and Rates of Change . . . . . . . 104
Summary:
Increasing
and
Decreasing
Functions; Concavity . . . . . . . . 106
REVIEW PROBLEMS . . . . . . . . . . . 109
STRENGTHEN YOUR UNDERSTANDING
113
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