Introductory & Intermediate Algebra for College Students (4th Edition)

1221 Pages·2012·33.56 MB·English

by  Robert F. Blitzer

Introductory &
Intermediate Algebra
for College Students
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FOURTH EDITION
Introductory &
Intermediate Algebra
for College Students
Annotated Instructor’s Edition
Robert Blitzer
Miami Dade College
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Material in this text from Blitzer, Robert F., Math For Your World, 1st Edition, © 2012. Reprinted by
permission of Pearson Education, Inc., Upper Saddle River, NJ.
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Library of Congress Cataloging-in-Publication Data
Blitzer, Robert.
Introductory & Intermediate algebra for college students / Robert Blitzer. —4th ed.
p. cm.
ISBN-13: 978-0-321-75894-1
ISBN-10: 0-321-75894-3
1. Algebra—Textbooks. I. Title.
QA152.3.B65 2013
512.9—dc22 2011006472
Copyright © 2013, 2009, 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.
1 2 3 4 5 6 7 8 9 10—QGD—15 14 13 12
ISBN 10: 0-321-75894-3
www.pearsonhighered.com ISBN 13: 978-0-321-75894-1
Table of Contents
Preface ix 2.6 Problem Solving in Geometry 168
To the Student xvii 2.7 Solving Linear Inequalities 182
About the Author xix Chapter 2 Group Project 198
1 Chapter 2 Summary 198
Variables, Real Numbers,
Chapter 2 Review Exercises 204
and Mathematical Models 1
Chapter 2 Test 207
1.1 Introduction to Algebra: Variables and Mathematical CumulativeReview Exercises (Chapters 1—2) 208
Models 2
1.2 Fractions in Algebra 14
1.3 The Real Numbers 32
1.4 Basic Rules of Algebra 44
Mid-Chapter Check Point—Section 1.1–Section 1.4 55
1.5 Addition of Real Numbers 56
1.6 Subtraction of Real Numbers 65
1.7 Multiplication and Division of Real Numbers 73
1.8 Exponents and Order of Operations 87
Chapter 1 Group Project 101
Chapter 1 Summary 102
Chapter 1 Review Exercises 108
Chapter 1 Test 111
2
Linear Equations and Inequalities
in One Variable 113
2.1 The Addition Property of Equality 114
2.2 The Multiplication Property of Equality 122
2.3 Solving Linear Equations 132
2.4 Formulas and Percents 144
Mid-Chapter Check Point—Section 2.1–Section 2.4 155
2.5 An Introduction to Problem Solving 156
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3
Linear Equations Chapter 4 Group Project 335
in Two Variables 209 Chapter 4 Summary 336
Chapter 4 Review Exercises 339
3.1 Graphing Linear Equations in Two Variables 210
Chapter 4 Test 341
3.2 Graphing Linear Equations Using Intercepts 223
CumulativeReview Exercises (Chapters 1—4) 342
3.3 Slope 234
5
3.4 The Slope-Intercept Form of the Equation of a Line 244
Exponents
Mid-Chapter Check Point—Section 3.1–Section 3.4 253
and Polynomials 343
3.5 The Point-Slope Form of the Equation of a Line 254
5.1 Adding and Subtracting Polynomials 344
Chapter 3 Group Project 265
5.2 Multiplying Polynomials 353
Chapter 3 Summary 266
5.3 Special Products 363
Chapter 3 Review Exercises 269
5.4 Polynomials in Several Variables 372
Chapter 3 Test 272
Mid-Chapter Check Point—Section 5.1–Section 5.4 380
CumulativeReview Exercises (Chapters 1—3) 273
5.5 Dividing Polynomials 381
4
Systems of 5.6 Long Division of Polynomials; Synthetic Division 390
Linear Equations 275 5.7 Negative Exponents and Scientific Notation 404
Chapter 5 Group Project 417
4.1 Solving Systems of Linear Equations by Graphing 276
Chapter 5 Summary 417
4.2 Solving Systems of Linear Equations by the Substitution
Method 288 Chapter 5 Review Exercises 421
4.3 Solving Systems of Linear Equations by the Addition Chapter 5 Test 423
Method 297 CumulativeReview Exercises (Chapters 1—5) 424
Mid-Chapter Check Point—Section 4.1–Section 4.3 306 6
Factoring
4.4 Problem Solving Using Systems of Equations 307
Polynomials 425
4.5 Systems of Linear Equations in Three Variables 324
6.1 The Greatest Common Factor and Factoring
by Grouping 426
6.2 Factoring Trinomials Whose Leading Coefficient Is 1 435
6.3 Factoring Trinomials Whose Leading Coefficient Is
Not 1 444
Mid-Chapter Check Point—Section 6.1–Section 6.3 452
6.4 Factoring Special Forms 452
6.5 A General Factoring Strategy 462
6.6 Solving Quadratic Equations by Factoring 470
Chapter 6 Group Project 483
Chapter 6 Summary 483
Chapter 6 Review Exercises 485
Chapter 6 Test 487
CumulativeReview Exercises (Chapters 1—6) 488
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9.3 Equations and Inequalities Involving Absolute Value 663
Mid-Chapter Check Point—Section 9.1–Section 9.3 673
9.4 Linear Inequalities in Two Variables 674
Chapter 9 Group Project 685
7 Chapter 9 Summary 685
Rational Chapter 9 Review Exercises 688
Expressions 489 Chapter 9 Test 689
7.1 Rational Expressions and Their Simplification 490 CumulativeReview Exercises (Chapters 1—9) 690
7.2 Multiplying and Dividing Rational Expressions 500 10
Radicals, Radical Functions,
7.3 Adding and Subtracting Rational Expressions with
and Rational Exponents 691
the Same Denominator 507
7.4 Adding and Subtracting Rational Expressions 10.1 Radical Expressions and Functions 692
with Different Denominators 515
10.2 Rational Exponents 705
Mid-Chapter Check Point—Section 7.1–Section 7.4 526
10.3 Multiplying and Simplifying Radical Expressions 715
7.5 Complex Rational Expressions 527
10.4 Adding, Subtracting, and Dividing Radical
7.6 Solving Rational Equations 535 Expressions 723
7.7 Applications Using Rational Equations and Mid-Chapter Check Point—Section 10.1–Section 10.4 731
Proportions 547
10.5 Multiplying with More Than One Term and Rationalizing
7.8 Modeling Using Variation 559 Denominators 732
Chapter 7 Group Project 572 10.6 Radical Equations 742
Chapter 7 Summary 572 10.7 Complex Numbers 752
Chapter 7 Review Exercises 578 Chapter 10 Group Project 762
Chapter 7 Test 580 Chapter 10 Summary 762
CumulativeReview Exercises (Chapters 1—7) 581 Chapter 10 Review Exercises 766
Mid-Textbook Check Point 582 Chapter 10 Test 768
8 CumulativeReview Exercises (Chapters 1—10) 769
Basics
of Functions 585
8.1 Introduction to Functions 586
8.2 Graphs of Functions 596
8.3 The Algebra of Functions 609
Mid-Chapter Check Point—Section 8.1–Section 8.3 618
8.4 Composite and Inverse Functions 619
Chapter 8 Group Project 633
Chapter 8 Summary 634
Chapter 8 Review Exercises 636
Chapter 8 Test 638
CumulativeReview Exercises (Chapters 1—8) 638
9
Inequalities
and Problem Solving 641
9.1 Reviewing Linear Inequalities and Using Inequalities
in Business Applications 642
9.2 Compound Inequalities 653
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11
Quadratic Equations Mid-Chapter Check Point—Section 12.1–Section 12.3 894
and Functions 771 12.4 Exponential and Logarithmic Equations 895
12.5 Exponential Growth and Decay; Modeling Data 909
11.1 The Square Root Property and Completing the Square;
Chapter 12 Group Project 922
Distance and Midpoint Formulas 772
Chapter 12 Summary 922
11.2 The Quadratic Formula 788
Chapter 12 Review Exercises 925
11.3 Quadratic Functions and Their Graphs 803
Chapter 12 Test 928
Mid-Chapter Check Point—Section 11.1–Section 11.3 821
CumulativeReview Exercises (Chapters 1—12) 929
11.4 Equations Quadratic in Form 822
13
Conic Sections and Systems
11.5 Polynomial and Rational Inequalities 830
of Nonlinear Equations 931
Chapter 11 Group Project 844
Chapter 11 Summary 845 13.1 The Circle 932
Chapter 11 Review Exercises 849 13.2 The Ellipse 939
Chapter 11 Test 851 13.3 The Hyperbola 951
CumulativeReview Exercises (Chapters 1—11) 852 Mid-Chapter Check Point—Section 13.1–Section 13.3 960
13.4 The Parabola; Identifying Conic Sections 961
12
Exponential and Logarithmic 13.5 Systems of Nonlinear Equations in Two Variables 973
Functions 855 Chapter 13 Group Project 984
Chapter 13 Summary 985
12.1 Exponential Functions 856
Chapter 13 Review Exercises 987
12.2 Logarithmic Functions 870
Chapter 13 Test 989
12.3 Properties of Logarithms 883
CumulativeReview Exercises (Chapters 1—13) 990
14
Sequences, Series, and the
Binomial Theorem 991
14.1 Sequences and Summation Notation 992
14.2 Arithmetic Sequences 1002
14.3 Geometric Sequences and Series 1012
Mid-Chapter Check Point—Section 14.1–Section 14.3 1028
14.4 The Binomial Theorem 1028
Chapter 14 Group Project 1036
Chapter 14 Summary 1037
Chapter 14 Review Exercises 1039
Chapter 14 Test 1041
CumulativeReview Exercises (Chapters 1—14) 1042
Appendices 1043
A Mean, Median, and Mode 1043
B Matrix Solutions to Linear Systems 1049
C Determinants and Cramer’s Rule 1058
D Where DidThat Come From? Selected Proofs 1067
Answers to Selected Exercises AA1
ApplicationsIndex AP1
SubjectIndexI1
Photo Credits C1
Preface
IntroductoryandIntermediateAlgebra for College Students, Fourth Edition, provides
comprehensive, in-depth coverage of the topics required in a course combining
the study of introductory and intermediate algebra. The book is written for college
students who have no previous experience in algebra and for those who need a
review of basic algebraic concepts before moving on to intermediate algebra. I wrote
the book to help diverse students, with different backgrounds and career plans, to
succeed in a combined introductory and intermediate algebra course. Introductory
andIntermediateAlgebra for College Students, Fourth Edition, has two primary goals:
1. To help students acquire a solid foundation in the skills and concepts of
introductory and intermediate algebra, without the repetition of topics in two
separate texts.
2. To show students how algebra can model and solve authentic real-world problems.
One major obstacle in the way of achieving these goals is the fact that very few
students actually read their textbook. This has been a regular source of frustration for
me and for my colleagues in the classroom. Anecdotal evidence gathered over years
highlights two basic reasons why students do not take advantage of their textbook:
(cid:114)(cid:1) “I’ll never use this information.”
(cid:114)(cid:1) “I can’t follow the explanations.”
I’ve written every page of the Fourth Edition with the intent of eliminating these two
objections. The ideas and tools I’ve used to do so are described in the features that
follow. These features and their benefits are highlighted for the student in “A Brief
Guide to Getting the Most from This Book,” which appears inside the front cover.
What’s New in the Fourth Edition?
(cid:114)(cid:1) New Applications and Real-World Data. I’m on a constant search for data that
can be used to illustrate unique algebraic applications. I researched hundreds of
books, magazines, newspapers, almanacs, and online sites to prepare the Fourth
Edition. Among the worked-out examples and exercises based on new data sets,
you’ll find applications involving stretching one’s life span, the emotional health of
college freshmen, changing attitudes toward marriage, American Idol’s viewership,
and the year humans become immortal.
(cid:114)(cid:1) Concept and Vocabulary Checks. The Fourth Edition contains more than 1500
new short-answer exercises, mainly fill-in-the-blank and true/false items, that
assess students’ understanding of the definitions and concepts presented in
each section. The Concept and Vocabulary Checks appear as separate features
preceding the Exercise Sets.
ix