Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

Using Fractional Notation

       95–100 Factor the greatest common factor (GCF) from each term and write the factored form.

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Solving Radical Equations

       101–110 Solve for x. Check for any extraneous solutions.

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Rationalizing Denominators

       111–120 Simplify by rationalizing the denominator.

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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 , find .

      122. Given , find .

      123. Given , find .

      124. Given , find .

      125. Given , find .

Determining