Showing Why Math Matters Gary Rockswold teaches algebra in context, answering the question, “Why am I learning this?” Going green Many activities, such as driving a car, watching television, riding a jet ski, or flying in an airplane, emit carbon dioxide into the air A commercial airliner, for example, emits 150 pounds of carbon dioxide for each passenger who flies 240 miles Understanding our environmental impact on the planet is becoming increasingly important Functions can be used to model and predict carbon emissions (See the Chapter opener on page 76 and Example from Section 2.1 on page 81.) How many songs will my iPod hold? The number of songs that will fit on your iPod depends on the size of its memory We can use the concept of slope to analyze memory requirements for storing music on iPods (See Example from Section 1.4 on page 49 to learn more.) Determining sunset times Whether we are traveling cross-country, driving a boat on a lake, or designing a solar power plant, the time of sunset can be important If we know the sunset time on two different days, can we make predictions about sunset times on other days? Using a linear function, we can often make accurate estimates (See Example from Section 2.4 on page 139.) Shooting free throws Is it better to shoot a free throw overhand or underhand? Mathematics can be used to improve an athlete’s performance Learn how parabolas, the angle of release, and the velocity of the basketball all play a role in determining whether the ball goes through the hoop (See the Chapter opener on page 169 to learn more.) Modeling movement of weather How meteorologists know where a cold front will be tomorrow? How they know that one city will be hit by a blizzard, and a city 100 miles away will get only flurries? Scientists model weather systems and make predictions by translating and transforming graphs on a weather map (Learn more in Section 3.5 on pages 222 and 238.) Waiting in line Have you ever noticed how a slight increase in the number of cars exiting a parking garage or trying to get through a construction zone can make your wait much longer? These long lines of waiting cars are subject to a nonlinear effect To make predictions about traffic congestion, highway engineers often use rational functions (See the application and Example in Section 4.6 on page 309 to learn more.) 4th edition ESSENTIALS OF C OLLEGE A LGEBRA with Modeling & Visualization This page intentionally left blank 4th edition ESSENTIALS OF C OLLEGE A LGEBRA with Modeling & Visualization Gary K Rockswold Minnesota State University, Mankato Addison-Wesley Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Executive Editor Anne Kelly Associate Content Editor Leah Goldberg, Dana Jones Bettez Editorial Assistant Brenden Berger Senior Managing Editor Karen Wernholm Production Project Manager Beth Houston Design Manager Andrea Nix Senior Design Supervisor Heather Scott Senior Media Producer Ceci Fleming Software Development Mary Durnwald, TestGen, and Rebecca Williams, MathXL Executive Marketing Manager Roxanne McCarley Marketing Assistant Katherine Minton Senior Author Support/Technology Specialist Joe Vetere Senior Manufacturing Buyer Carol Melville Text Design, Composition, and Illustrations Nesbitt Graphics, Inc Cover Designer Nancy Goulet, studio;wink Cover photo: Jim Wehje/Photodisc/Getty Images Photo credits appear on page P-1 Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps Library of Congress Cataloging-in-Publication Data Rockswold, Gary K Essentials of college algebra with modeling and visualization / Gary K Rockswold 4th ed p cm ISBN-13: 978-0-321-71528-9 (student edition) ISBN-10: 0-321-71528-4 (student edition) Algebra Textbooks Algebraic functions Textbooks Mathematical models Textbooks I Title QA154.3.R635 2012 512.9 dc22 2010040485 Copyright © 2012, 2008, 2006, 2002 Pearson Education, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher Printed in the United States of America For information on obtaining permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.pearsoned.com/legal/permissions.htm 10—WCD—14 13 12 11 10 www.pearsonhighered.com ISBN-10: 0-321-71528-4 ISBN-13: 978-0-321-71528-9 In memory of my friend and colleague Larry Pearson, who is deeply missed by many This page intentionally left blank Contents Preface xiii Introduction to Functions and Graphs 1.1 Numbers, Data, and Problem Solving Sets of Numbers Problem Solving ■ 1.2 Visualizing and Graphing Data One-Variable Data Midpoint Formula ■ Order of Operations ■ ■ Scientific Notation ■ 12 Two-Variable Data ■ The Distance Formula ■ The Circles ■ Graphing with a Calculator (Optional) Checking Basic Concepts for Sections 1.1 and 1.2 28 1.3 Functions and Their Representations 28 Basic Concepts ■ Representations of Functions ■ Formal Definition of a Function ■ Graphing Calculators and Functions (Optional) ■ Identifying Functions ■ Functions Represented by Diagrams and Equations 1.4 Types of Functions 45 Constant Functions ■ Linear Functions Nonlinear Functions ■ Slope as a Rate of Change Checking Basic Concepts for Sections 1.3 and 1.4 1.5 Functions and Their Rates of Change Increasing and Decreasing Functions Change ■ The Difference Quotient ■ ■ 55 56 Interval Notation ■ Average Rate of Checking Basic Concepts for Section 1.5 67 Chapter Summary 67 Chapter Review Exercises 71 Chapter Extended and Discovery Exercises 74 Linear Functions and Equations 76 2.1 Linear Functions and Models 77 Functions as Models ■ Representations of Linear Functions ■ Modeling with Linear Functions ■ Piecewise-Defined Functions ■ The Greatest Integer Function ■ Linear Regression (Optional) vii ... Community College Metropolitan State College of Denver Augustana College Paradise Valley Community College Florida Community College, Kent Campus Henderson State University Holyoke Community College. .. Community College Jefferson Community College College of Lake County Pellissippi State Community College Front Range Community College, Larimer Middle Tennessee State University Floyd College at... of Functions AP-19 Appendix C: Partial Fractions AP-22 Bibliography B-1 Answers to Selected Exercises A-1 Photo Credits P-1 Index of Applications I-1 Index I-5 Preface Essentials of College Algebra