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102.
103.
104.
105.
106.
107.
108.
109.
110.
Rationalizing Denominators
111–120 Simplify by rationalizing the denominator.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
Chapter 3
Function Basics
A function is a special type of rule or relationship. The difference between a function and a relation is that a function has exactly one output value (from the range) for every input value (from the domain). Functions are very useful when you’re describing trends in business, heights of objects shot from a cannon, times required to complete a task, and so on. Functions have some special properties and operations that allow for investigation into what happens when you change the rule.
The Problems You’ll Work On
In this chapter, you’ll work with functions and function operations in the following ways:
Writing and using function notation
Determining the domain and range of different types of functions
Recognizing even and odd functions
Checking on whether a function is one-to-one
Finding inverses of one-to-one functions
Performing the basic operations on functions and function rules
Working with the composition of functions and the difference quotient
What to Watch Out For
Don’t let common mistakes trip you up; keep in mind that when working with functions, your challenges will include
Following the order of operations when evaluating functions
Determining which values need to be excluded from a function’s domain
Working with negative signs correctly when checking for even and odd functions
Being sure a function is one-to-one before trying to determine an inverse
Correctly applying function rules when performing function composition
Raising binomials to higher powers and including all the terms
Using Function Notation to Evaluate Function Values
121−125 Evaluate the function for the given value.
121. Given
122. Given
123. Given
124. Given
125. Given
Determining the Domain and Range of a Function
126−135 Find the domain and range for the function.
126.
127.
