Tussy gustafson elementary intermediate algebra 4th txtbk

www.elsolucionario.net www.elsolucionario.net ELEMENTARY AND INTERMEDIATE FOURTH ALGEBRA EDITION Alan S Tussy ■ R David Gustafson Rock Valley College Harry Shrunk © 1972 Christo Citrus College Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States www.elsolucionario.net Elementary and Intermediate Algebra, Fourth Edition Alan S Tussy, R David Gustafson Executive Editor: Charlie Van Wagner Development Editor: Danielle Derbenti Assistant Editor: Laura Localio Editorial Assistant: Lynh Pham Technology Project Manager: Jessica Kuhn Senior Marketing Manager: Greta Kleinert Marketing Assistant: Cassandra Cummings Marketing Communications Manager: Darlene Amidon-Brent Project Manager, Editorial Production: Cheryll Linthicum Creative Director: Rob Hugel Senior Art Director: Vernon T Boes Print Buyer: Judy Inouye Permissions Editor: Bob Kauser © 2009, 2005 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means, graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Library of Congress Control Number: 2008923496 ISBN-13: 978-0-495-38961-3 ISBN-10: 0-495-38961-7 Brooks Cole 10 Davis Drive Belmont, CA 94002-3098 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Production Service: Graphic World Inc Text Designer: Terri Wright Photo Researcher: Terri Wright Illustrator: Lori Heckelman Cover Designer: Terri Wright Cover Image: Harry Shrunk © 1972 Christo Cover Printer: Transcontinental Printing / Interglobe Compositor: Graphic World Inc Printed in Canada 12 11 10 09 08 www.elsolucionario.net In memory of my mother, Jeanene, and in honor of my dad, Bill —AST In memory of my teacher and mentor, Professor John Finch —RDG www.elsolucionario.net This page intentionally left blank www.elsolucionario.net CONTENTS AN INTRODUCTION TO ALGEBRA 1.1 1.2 1.3 1.4 1.5 1.6 Introducing the Language of Algebra Fractions 11 The Real Numbers 25 Adding Real Numbers; Properties of Addition 35 Subtracting Real Numbers 44 Multiplying and Dividing Real Numbers; Multiplication and Division Properties 51 1.7 Exponents and Order of Operations 62 1.8 Algebraic Expressions 74 1.9 Simplifying Algebraic Expressions Using Properties of Real Numbers 85 Chapter Summary and Review 96 Chapter Test 105 Group Project 106 EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING 107 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Solving Equations Using Properties of Equality 108 More about Solving Equations 119 Applications of Percent 129 Formulas 138 Problem Solving 152 More about Problem Solving 162 Solving Inequalities 173 Chapter Summary and Review 187 Chapter Test 194 Group Project 196 GRAPHING LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES; FUNCTIONS 197 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Graphing Using the Rectangular Coordinate System 198 Graphing Linear Equations 208 Intercepts 220 Slope and Rate of Change 232 Slope–Intercept Form 247 Point–Slope Form 258 Graphing Linear Inequalities 268 An Introduction to Functions 279 Chapter Summary and Review 293 Chapter Test 302 Group Project 304 Cumulative Review 305 v www.elsolucionario.net vi CONTENTS SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES 307 4.1 4.2 4.3 4.4 4.5 Solving Systems of Equations by Graphing 308 Solving Systems of Equations by Substitution 319 Solving Systems of Equations by Elimination (Addition) 330 Problem Solving Using Systems of Equations 341 Solving Systems of Linear Inequalities 356 Chapter Summary and Review 366 Chapter Test 372 Group Project 373 EXPONENTS AND POLYNOMIALS 375 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Rules for Exponents 376 Zero and Negative Exponents 389 Scientific Notation 399 Polynomials 406 Adding and Subtracting Polynomials 416 Multiplying Polynomials 427 Special Products 437 Dividing Polynomials 446 Chapter Summary and Review 456 Chapter Test 464 Group Project 465 Cumulative Review 466 FACTORING AND QUADRATIC EQUATIONS 469 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 The Greatest Common Factor; Factoring by Grouping 470 Factoring Trinomials of the Form x2 ϩ bx ϩ c 481 Factoring Trinomials of the Form ax ϩ bx ϩ c 493 Factoring Perfect-Square Trinomials and the Differences of Two Squares 504 Factoring the Sum and Difference of Two Cubes 512 A Factoring Strategy 517 Solving Quadratic Equations by Factoring 522 Applications of Quadratic Equations 531 Chapter Summary and Review 540 Chapter Test 547 Group Project 549 RATIONAL EXPRESSIONS AND EQUATIONS 551 7.1 7.2 7.3 Simplifying Rational Expressions 552 Multiplying and Dividing Rational Expressions 562 Adding and Subtracting with Like Denominators; Least Common Denominators 572 7.4 Adding and Subtracting with Unlike Denominators 582 7.5 Simplifying Complex Fractions 591 7.6 Solving Rational Equations 600 7.7 Problem Solving Using Rational Equations 609 7.8 Proportions and Similar Triangles 620 Chapter Summary and Review 632 Chapter Test 640 Group Project 642 Cumulative Review 642 www.elsolucionario.net CONTENTS vii TRANSITION TO INTERMEDIATE ALGEBRA 645 8.1 8.2 8.3 8.4 8.5 Review of Solving Linear Equations, Formulas, and Linear Inequalities 646 Solving Compound Inequalities 660 Solving Absolute Value Equations and Inequalities 672 Review of Factoring Methods: GCF, Grouping, Trinomials 685 Review of Factoring Methods: The Difference of Two Squares; the Sum and Difference of Two Cubes 697 8.6 Review of Rational Expressions and Rational Equations 705 8.7 Review of Linear Equations in Two Variables 720 8.8 Functions 736 8.9 Variation 756 Chapter Summary and Review 765 Chapter Test 781 Group Project 783 Cumulative Review 784 RADICAL EXPRESSIONS AND EQUATIONS 787 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Radical Expressions and Radical Functions 788 Rational Exponents 804 Simplifying and Combining Radical Expressions 817 Multiplying and Dividing Radical Expressions 829 Solving Radical Equations 842 Geometric Applications of Radicals 854 Complex Numbers 867 Chapter Summary and Review 880 Chapter Test 889 Group Project 891 10 QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES 893 10.1 10.2 10.3 10.4 10.5 The Square Root Property and Completing the Square 894 The Quadratic Formula 907 The Discriminant and Equations That Can Be Written in Quadratic Form 919 Quadratic Functions and Their Graphs 929 Quadratic and Other Nonlinear Inequalities 945 Chapter Summary and Review 957 Chapter Test 964 Group Project 966 Cumulative Review 967 11 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 971 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 Algebra and Composition of Functions 972 Inverse Functions 984 Exponential Functions 996 Base-e Exponential Functions 1012 Logarithmic Functions 1021 Base-e Logarithmic Functions 1035 Properties of Logarithms 1043 Exponential and Logarithmic Equations 1055 Chapter Summary and Review 1068 Chapter Test 1079 Group Project 1080 www.elsolucionario.net viii CONTENTS 12 MORE ON SYSTEMS OF EQUATIONS 1083 12.1 12.2 12.3 12.4 12.5 Solving Systems of Equations in Two Variables 1084 Solving Systems of Equations in Three Variables 1103 Problem Solving Using Systems of Thee Equations 1114 Solving Systems of Equations Using Matrices 1122 Solving Systems of Equations Using Determinants 1134 Chapter Summary and Review 1145 Chapter Test 1154 Group Project 1155 Cumulative Review 1156 13 CONIC SECTIONS; MORE GRAPHING 1161 13.1 13.2 13.3 13.4 The Circle and the Parabola 1162 The Ellipse 1176 The Hyperbola 1186 Solving Nonlinear Systems of Equations 1197 Chapter Summary and Review 1205 Chapter Test 1210 Group Project 1212 14 MISCELLANEOUS TOPICS 1213 14.1 14.2 14.3 The Binomial Theorem 1214 Arithmetic Sequences and Series 1224 Geometric Sequences and Series 1235 Chapter Summary and Review 1248 Chapter Test 1252 Group Project 1253 Cumulative Review 1254 APPENDIXES APPENDIX 1: Roots and Powers A-1 APPENDIX 2: Synthetic Division A-2 APPENDIX 3: Answers to Selected Exercises A-9 INDEX I-1 www.elsolucionario.net ...www.elsolucionario.net ELEMENTARY AND INTERMEDIATE FOURTH ALGEBRA EDITION Alan S Tussy ■ R David Gustafson Rock Valley College Harry Shrunk © 1972 Christo Citrus... Spain • United Kingdom • United States www.elsolucionario.net Elementary and Intermediate Algebra, Fourth Edition Alan S Tussy, R David Gustafson Executive Editor: Charlie Van Wagner Development... entrance to all the content that accompanies Tussy/ Gustafson? ??s Elementary Algebra, Fourth Edition, within CengageNOW WEBSITE academic.cengage.com/math /tussy Visit us on the web for access to a