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Chapter 5

Functions

A function is a relationship in which there is exactly one output value for each input value. The functions used in algebra incorporate all sorts of operations — from addition and subtraction to absolute value and factorial. Functions might be restricted as to their input values; the input values constitute the domain. And a function may have a limited number of output values (its range) due to the way the operations are performed on the input values.

The Problems You’ll Work On

In this chapter, you’ll work with functions in the following ways:

 Determining the domain and range from the function equation

 Recognizing odd and even functions

 Categorizing some functions as one-to-one

 Performing function composition

 Finding inverses of functions

 Working with piecewise functions

What to Watch Out For

Don’t let common mistakes trip you up; watch for the following when working with functions:

 Making the correct exclusions in the domains of functions that have radicals or fractions in their function rule

 Distributing factors correctly when performing function compositions

 Squaring and cubing binomials correctly when performing function compositions

 Working through the correct steps when solving for a function’s inverse

Determining a Function’s Domain and Range

241–250 Find the domain and range of the function.

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Finding Inverses of Functions

251–260 Find the inverse of the function.

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Recognizing Even and Odd Functions

261–270 Determine if the function is even or odd and whether it’s one-to-one.

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Performing the Composition Operation on Functions

271–280 Find the composition of given f and g.

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Creating a Difference-Quotient and Simplifying

281–290 Given f(x), find the difference-quotient _.

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Evaluating Piecewise Functions for Particular Inputs

291–300 Given the piecewise function, evaluate as requested.

291. Evaluate f(1) in

292. Evaluate f(-1) in

293. Evaluate f(2) in

294. Evaluate f(0) in

295. Evaluate f(–1) in

296. Evaluate f(–4) in

297. Evaluate f(–5) in

298. Evaluate f(51) in

299. Evaluate f(0) in

300. Evaluate f(4) in