Intermediate algebra

845 Pages·2020·60.465 MB·English

by  John Hornsby, Terry McGinnis, Margaret L. Lial

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Intermediate
EDITION
13
Algebra
Margaret L. Lial
American River College
John Hornsby
University of New Orleans
Terry McGinnis
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Library of Congress Cataloging-in-Publication Data
Names: Lial, Margaret L., author. | Hornsby, John, 1949- author. | McGinnis,
Terry, author.
Title: Intermediate algebra / Margaret L. Lial (American River College), John
Hornsby (University of New Orleans), Terry McGinnis.
Description: 13th edition. | Boston : Pearson, [2020] | Includes index.
Identifiers: LCCN 2018048199 | ISBN 9780134895987 (student edition) | ISBN 0134895983
(student edition) | ISBN 9780134996752 (annotated instructor edition) | ISBN
0134996755 (annotated instructor edition)
Subjects: LCSH: Algebra--Textbooks.
Classification: LCC QA152.3 .L534 2020 | DDC 512.9--dc23
LC record available at https://lccn.loc.gov/2018048199
1 18
ISBN 13: 978-0-13-489598-7
ISBN 10: 0-13-489598-3
CONTENTS
Preface vii
Study Skills S-1
STUDY SKILL 1 Using Your Math Text S-1 STUDY SKILL 6 Managing Your Time S-6
STUDY SKILL 2 Reading Your Math Text S-2 STUDY SKILL 7 Reviewing a Chapter S-7
STUDY SKILL 3 Taking Lecture Notes S-3 STUDY SKILL 8 Taking Math Tests S-8
STUDY SKILL 4 Completing Your Homework S-4 STUDY SKILL 9 Analyzing Your Test Results S-9
STUDY SKILL 5 Using Study Cards S-5 STUDY SKILL 10 Preparing for Your Math Final
Exam S-10
R Review of the Real Number System 1
R.1 Fractions, Decimals, and Percents 1 R.5 Properties of Real Numbers 45
R.2 Basic Concepts from Algebra 14 Chapter R Summary 52
R.3 Operations on Real Numbers 26 Chapter R Test 54
R.4 Exponents, Roots, and Order of Operations 36
1 Linear Equations, Inequalities, and Applications 55
1.1 Linear Equations in One Variable 56 1.7 Absolute Value Equations and Inequalities 125
1.2 Formulas and Percent 65 SUMMARY EXERCISES Solving Linear and Absolute Value
1.3 Applications of Linear Equations 78 Equations and Inequalities 136
1.4 Further Applications of Linear Equations 92 Chapter 1 Summary 137
Chapter 1 Review Exercises 142
SUMMARY EXERCISES Applying Problem-Solving
Chapter 1 Mixed Review Exercises 145
Techniques 101
Chapter 1 Test 146
1.5 Linear Inequalities in One Variable 103
Chapters R and 1 Cumulative Review
1.6 Set Operations and Compound Inequalities 116
Exercises 148
2 Linear Equations, Graphs, and Functions 149
2.1 Linear Equations in Two Variables 150 2.5 Introduction to Relations and Functions 199
2.2 The Slope of a Line 161 2.6 Function Notation and Linear Functions 210
2.3 Writing Equations of Lines 176 Chapter 2 Summary 219
SUMMARY EXERCISES Finding Slopes and Equations Chapter 2 Review Exercises 222
of Lines 191 Chapter 2 Mixed Review Exercises 224
Chapter 2 Test 225
2.4 Linear Inequalities in Two Variables 192
Chapters R–2 Cumulative Review Exercises 227
iii
iv Contents
3 Systems of Linear Equations 229
3.1 Systems of Linear Equations in Two Chapter 3 Summary 270
Variables 230 Chapter 3 Review Exercises 273
3.2 Systems of Linear Equations in Three Chapter 3 Mixed Review Exercises 275
Variables 245 Chapter 3 Test 276
Chapters R–3 Cumulative Review
3.3 Applications of Systems of Linear
Exercises 277
Equations 254
4 Exponents, Polynomials, and Polynomial Functions 279
4.1 Integer Exponents 280 4.6 Dividing Polynomials 324
4.2 Scientific Notation 290 Chapter 4 Summary 331
4.3 Adding and Subtracting Polynomials 296 Chapter 4 Review Exercises 334
Chapter 4 Mixed Review Exercises 337
4.4 Polynomial Functions, Graphs, and
Chapter 4 Test 337
Composition 302
Chapters R–4 Cumulative Review
4.5 Multiplying Polynomials 315
Exercises 338
5 Factoring 341
5.1 Greatest Common Factors and Factoring Chapter 5 Summary 376
by Grouping 342 Chapter 5 Review Exercises 379
5.2 Factoring Trinomials 348 Chapter 5 Mixed Review Exercises 381
Chapter 5 Test 382
5.3 Special Factoring 356
Chapters R–5 Cumulative Review
5.4 A General Approach to Factoring 363
Exercises 382
5.5 Solving Quadratic Equations Using
the Zero-Factor Property 367
6 Rational Expressions and Functions 385
6.1 Rational Expressions and Functions; Multiplying 6.5 Applications of Rational Expressions 421
and Dividing 386 6.6 Variation 433
6.2 Adding and Subtracting Rational Chapter 6 Summary 443
Expressions 396 Chapter 6 Review Exercises 447
6.3 Complex Fractions 405 Chapter 6 Mixed Review Exercises 449
6.4 Equations with Rational Expressions Chapter 6 Test 450
and Graphs 411 Chapters R–6 Cumulative Review
Exercises 452
SUMMARY EXERCISES S implifying Rational Expressions vs.
Solving Rational Equations 419
Contents v
7 Roots, Radicals, and Root Functions 455
7.1 Radical Expressions and SUMMARY EXERCISES Performing Operations with Radicals
Graphs 456 and Rational Exponents 502
7.2 Rational Exponents 464 7.6 Solving Equations with Radicals 503
7.3 Simplifying Radicals, the Distance 7.7 Complex Numbers 510
Formula, and Circles 473 Chapter 7 Summary 518
7.4 Adding and Subtracting Radical Chapter 7 Review Exercises 523
Expressions 487 Chapter 7 Mixed Review Exercises 526
7.5 Multiplying and Dividing Radical Chapter 7 Test 527
Expressions 492 Chapters R–7 Cumulative Review
Exercises 528
8 Quadratic Equations, Inequalities, and Functions 531
8.1 The Square Root Property and 8.6 More about Parabolas and Their
Completing the Square 532 Applications 579
8.2 The Quadratic Formula 541 8.7 Polynomial and Rational Inequalities 590
8.3 Equations That Lead to Quadratic Methods 549 Chapter 8 Summary 599
SUMMARY EXERCISES Applying Methods for Solving Chapter 8 Review Exercises 603
Quadratic Equations 560 Chapter 8 Mixed Review Exercises 606
Chapter 8 Test 607
8.4 Formulas and Further Applications 561
Chapters R–8 Cumulative Review
8.5 Graphs of Quadratic Functions 570
Exercises 609
9 Inverse, Exponential, and Logarithmic Functions 611
9.1 Inverse Functions 612 Chapter 9 Summary 663
9.2 Exponential Functions 621 Chapter 9 Review Exercises 667
Chapter 9 Mixed Review Exercises 670
9.3 Logarithmic Functions 630
Chapter 9 Test 672
9.4 Properties of Logarithms 639
Chapters R–9 Cumulative Review
9.5 Common and Natural Logarithms 646
Exercises 673
9.6 Exponential and Logarithmic Equations; Further
Applications 654
10 Nonlinear Functions, Conic Sections, and Nonlinear Systems 677
10.1 Additional Graphs of Functions 678 Chapter 10 Summary 715
10.2 Circles Revisited and Ellipses 684 Chapter 10 Review Exercises 718
Chapter 10 Mixed Review Exercises 720
10.3 Hyperbolas and Functions Defined
Chapter 10 Test 721
by Radicals 694
Chapters R–10 Cumulative Review
10.4 Nonlinear Systems of Equations 702
Exercises 722
10.5 Second-Degree Inequalities and
Systems of Inequalities 708
vi Contents
11 Further Topics in Algebra 725
11.1 Sequences and Series 726 Chapter 11 Summary 756
11.2 Arithmetic Sequences 732 Chapter 11 Review Exercises 759
Chapter 11 Mixed Review Exercises 760
11.3 Geometric Sequences 740
Chapter 11 Test 761
11.4 The Binomial Theorem 750
Chapters R–11 Cumulative Review
Exercises 762
Appendix Synthetic Division 765
Answers to Selected Exercises A-1
Photo Credits C-1
Index I-1
PREFACE
now include a Now Try This section to help students imple-
WELCOME TO THE 13TH EDITION
ment the specific skill.
The first edition of Marge Lial’s Intermediate Algebra
was published in 1972, and now we are pleased to present REVISED EXPOSITION With each edition of the text, we con-
tinue to polish and improve discussions and presentations
the 13th edition—with the same successful, well-rounded
of topics to increase readability and student understanding.
framework that was established 50 years ago and updated
This edition is no exception.
to meet the needs of today’s students and professors. The
names Lial and Miller, two faculty members from American
NEW FIGURES AND DIAGRAMS For visual learners, we have
River College in Sacramento, California, have become syn-
included more than 50 new mathematical figures, graphs, and
onymous with excellence in Developmental Mathematics,
diagrams, including several new “hand drawn” style graphs.
Precalculus, Finite Mathematics, and Applications-Based
These are meant to suggest what a student who is graphing
Calculus.
with paper and pencil should obtain. We use this style when
With Chuck Miller’s passing in 1986, Marge Lial was
introducing a particular type of graph for the first time.
joined by a team of carefully selected coauthors who part-
nered with her. John Hornsby (University of New Orleans) ENHANCED USE OF PEDAGOGICAL COLOR We have thor-
joined Marge in this capacity in 1992, and in 1999, Terry oughly reviewed the use of pedagogical color in discussions
McGinnis became part of this developmental author team. and examples and have increased its use whenever doing so
Since Marge’s passing in 2012, John and Terry have dedi- would enhance concept development, emphasize important
cated themselves to carrying on the Lial/Miller legacy. steps, or highlight key procedures.
In the preface to the first edition of Intermediate
Algebra, Marge Lial wrote INCREASED Concept Check AND WHAT WENT WRONG?
EXERCISES The number of Concept Check exercises, which
“ . . . the strongest theme . . . is a combination of
facilitate students’ mathematical thinking and conceptual
readability and suitability for the book’s intended
understanding, and which begin each exercise set, has been
audience: students who are not completely self-
increased. We have also more than doubled the number
confident in mathematics as they come to the course,
of  WHAT WENT WRONG? exercises that highlight com-
but who must be self-confident and proficient . . . by
mon student errors.
the end of the course.”
INCREASED RELATING CONCEPTS EXERCISES We have
Today’s Lial author team upholds these same standards. With
doubled the number of these flexible groups of exercises,
the publication of the 13th edition of Intermediate Algebra,
which are located at the end of many exercise sets. These
we proudly present a complete course program for students
sets of problems were specifically written to help students
who need developmental algebra. Revisions to the core text,
tie concepts together, compare and contrast ideas, identify
working in concert with such innovations in the MyLab Math
and describe patterns, and extend concepts to new situations.
course as Skill Builder and Learning Catalytics, combine to
They may be used by individual students or by pairs or small
provide superior learning opportunities appropriate for all
groups working collaboratively. All answers to these exer-
types of courses (traditional, hybrid, online).
cises appear in the student answer section.
We hope you enjoy using it as much as we have enjoyed
writing it. We welcome any feedback that you have as you
ENHANCED MYLAB MATH RESOURCES MyLab exercise cov-
review and use this text.
erage in the revision has been expanded, and video coverage
has also been expanded and updated to a modern format for
today’s students. WHAT WENT WRONG? problems and all
WHAT’S NEW IN THIS EDITION?
RELATING CONCEPTS exercise sets (both even- and odd-
We are pleased to offer the following new features and numbered problems) are now assignable in MyLab Math.
resources in the text and MyLab.
SKILL BUILDER These exercises offer just-in-time additional
IMPROVED STUDY SKILLS These special activities are now adaptive practice in MyLab Math. The adaptive engine
grouped together at the front of the text, prior to Chapter R. tracks student performance and delivers, to each individual,
Study Skills Reminders that refer students to specific Study questions that adapt to his or her level of understanding. This
Skills are found liberally throughout the text. Many Study Skills new feature enables instructors to assign fewer questions for
vii
viii Preface
homework, allowing students to complete as many or as few Identifying functions and domains from equations
questions as they need. (Section 2.6)
LEARNING CATALYTICS This new student response tool uses Determining strategies for factoring polynomials
students’ own devices to engage them in the learning process. (Section 5.4)
Problems that draw on prerequisite skills are included at the
Solving quadratic equations with double solutions
beginning of each section to gauge student readiness for the
(Section 5.5)
section. Accessible through MyLab Math and customizable
to instructors’ specific needs, these problems can be used to Solving rational equations (Section 6.4)
generate class discussion, promote peer-to-peer learning, and
Concepts and relationships among real numbers,
provide real-time feedback to instructors. More information
nonreal complex numbers, and imaginary numbers;
can be found via the Learning Catalytics link in MyLab Math.
simplifying powers of i (Section 7.7)
Specific exercises notated in the text can be found by search-
ing LialIntermediate# where the # is the chapter number. Solving quadratic equations using the quadratic for-
mula (Section 8.2)
Solving exponential and logarithmic equations
CONTENT CHANGES
(Sections 9.2, 9.3)
Specific content changes include the following:
● Exercise sets have been scrutinized and updated with a
LIAL DEVELOPMENTAL HALLMARK FEATURES
renewed focus on conceptual understanding and skill de-
velopment. Even and odd pairing of the exercises, an im- We have enhanced the following popular features, each of
portant feature of the text, has been carefully reviewed. which is designed to increase ease of use by students and/
or instructors.
● Real world data in all examples and exercises and their
accompanying graphs has been updated. ● Emphasis on Problem-Solving We introduce our six-
step problem-solving method in Chapter 2 and integrate
● An increased emphasis on fractions, decimals, and per-
it throughout the text. The six steps, Read, Assign a
cents appears throughout the text. Chapter R begins with
Variable, Write an Equation, Solve, State the Answer,
a new section that thoroughly reviews these topics. And
and Check, are emphasized in boldface type and
we have included an all-new set of Cumulative Review
repeated in examples and exercises to reinforce the
Exercises, many of which focus on fractions, decimals,
problem-solving process for students. We also provide
and percents, at the end of Chapter 1. Sets of Cumulative
students with PROBLEM-SOLVING HINT boxes that feature
Review Exercises in subsequent chapters now begin with
helpful problem-solving tips and strategies.
new exercises that review skills related to these topics.
● Helpful Learning Objectives We begin each section
● Solution sets of linear inequalities in Sections 1.5–1.7
with clearly stated, numbered objectives, and the in-
are now graphed first before writing them using interval
cluded material is directly keyed to these objectives so
notation.
that students and instructors know exactly what is cov-
● Scientific notation is covered in a separate section in ered in each section.
Chapter 4.
● Cautions and Notes One of the most popular features of
● Chapters 10 and 11 on Nonlinear Functions, Conic previous editions is our inclusion of information marked
Sections, Nonlinear Systems, and Further Topics in ! CAUTION and NOTE to warn students about common
Algebra, previously available online in MyLab Math, errors and to emphasize important ideas throughout the
are now included in the text. The material has been fully exposition. The updated text design makes them easy
revised and updated. to spot.
● Presentations of the following topics have been en- ● Comprehensive Examples The new edition features
hanced and expanded, often including new examples a multitude of step-by-step, worked-out examples
and exercises: that include pedagogical color, helpful side com-
ments, and special pointers. We give special attention
Evaluating exponential expressions (Section R.4)
to checking example solutions—more checks, desig-
Geometric interpretation of slope as rise/run (Sec- nated using a special CHECK tag and ✓, are included
tion 2.2) than in past editions.
Solving systems of linear equations in three variables ● More Pointers There are more pointers in examples and
(Section 3.2) discussions throughout this edition of the text. They