Intermediate algebra

1117 Pages·2009·88.95 MB·English

by  Alan S Tussy

INTERMEDIATE
ALGEBRA
FOURTH
EDITION
Alan S. Tussy ■ R. David Gustafson
Citrus College Rock Valley College
Christo
© 1991
Volz
Wolfgang
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Intermediate Algebra, Fourth Edition © 2009, 2005Brooks/Cole, Cengage Learning
Alan S. Tussy, R. David Gustafson
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1 2 3 4 5 6 7 12 11 10 09 08
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
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CONTENTS
1
A REVIEW OF BASIC ALGEBRA 1
1.1 The Language of Algebra 2
1.2 The Real Numbers 10
1.3 Operations with Real Numbers 23
1.4 Simplifying Algebraic Expressions Using Properties of Real Numbers 37
1.5 Solving Linear Equations Using Properties of Equality 49
1.6 Solving Formulas; Geometry 63
1.7 Using Equations to Solve Problems 75
1.8 More about Problem Solving 86
Chapter Summary and Review 102
Chapter Test 113
Group Project 115
2
GRAPHS, EQUATIONS OF LINES, AND FUNCTIONS 117
2.1 The Rectangular Coordinate System 118
2.2 Graphing Linear Equations in Two Variables 132
2.3 Rate of Change and the Slope of a Line 146
2.4 Writing Equations of Lines 161
2.5 An Introduction to Functions 176
2.6 Graphs of Functions 192
Chapter Summary and Review 206
Chapter Test 216
Group Project 218
Cumulative Review 218
3
SYSTEMS OF EQUATIONS 221
3.1 Solving Systems of Equations by Graphing 222
3.2 Solving Systems of Equations Algebraically 235
3.3 Problem Solving Using Systems of Two Equations 246
3.4 Solving Systems of Equations in Three Variables 263
3.5 Problem Solving Using Systems of Three Equations 275
3.6 Solving Systems of Equations Using Matrices 282
3.7 Solving Systems of Equations Using Determinants 294
Chapter Summary and Review 305
Chapter Test 314
Group Project 315
Cumulative Review 316
v
vi CONTENTS
4
INEQUALITIES 319
4.1 Solving Linear Inequalities in One Variable 320
4.2 Solving Compound Inequalities 335
4.3 Solving Absolute Value Equations and Inequalities 347
4.4 Linear Inequalities in Two Variables 360
4.5 Systems of Linear Inequalities 370
Chapter Summary and Review 380
Chapter Test 387
Group Project 389
Cumulative Review 390
5
EXPONENTS, POLYNOMIALS, AND POLYNOMIAL FUNCTIONS 393
5.1 Exponents 394
5.2 Scientific Notation 408
5.3 Polynomials and Polynomial Functions 417
5.4 Multiplying Polynomials 434
5.5 The Greatest Common Factor and Factoring by Grouping 447
5.6 Factoring Trinomials 459
5.7 The Difference of Two Squares; the Sum and Difference of Two Cubes 473
5.8 Summary of Factoring Techniques 483
5.9 Solving Equations by Factoring 488
Chapter Summary and Review 503
Chapter Test 512
Group Project 514
6
RATIONAL EXPRESSIONS AND EQUATIONS 515
6.1 Rational Functions and Simplifying Rational Expressions 516
6.2 Multiplying and Dividing Rational Expressions 530
6.3 Adding and Subtracting Rational Expressions 542
6.4 Simplifying Complex Fractions 554
6.5 Dividing Polynomials 565
6.6 Synthetic Division 576
6.7 Solving Rational Equations 584
6.8 Problem Solving Using Rational Equations 596
6.9 Proportion and Variation 606
Chapter Summary and Review 622
Chapter Test 634
Group Project 635
CONTENTS vii
7
RADICAL EXPRESSIONS AND EQUATIONS 641
7.1 Radical Expressions and Radical Functions 642
7.2 Rational Exponents 658
7.3 Simplifying and Combining Radical Expressions 671
7.4 Multiplying and Dividing Radical Expressions 683
7.5 Solving Radical Equations 696
7.6 Geometric Applications of Radicals 708
7.7 Complex Numbers 721
Chapter Summary and Review 734
Chapter Test 743
Group Project 745
8
QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES 747
8.1 The Square Root Property and Completing the Square 748
8.2 The Quadratic Formula 761
8.3 The Discriminant and Equations That Can Be Written in Quadratic Form 773
8.4 Quadratic Functions and Their Graphs 783
8.5 Quadratic and Other Nonlinear Inequalities 799
Chapter Summary and Review 811
Chapter Test 818
Group Project 820
Cumulative Review 821
9
EXPONENTIAL AND LOGARITHMIC FUNCTIONS 825
9.1 Algebra and Composition of Functions 826
9.2 Inverse Functions 838
9.3 Exponential Functions 850
9.4 Base-eExponential Functions 866
9.5 Logarithmic Functions 875
9.6 Base-eLogarithmic Functions 889
9.7 Properties of Logarithms 897
9.8 Exponential and Logarithmic Equations 909
Chapter Summary and Review 922
Chapter Test 933
Group Project 934
viii CONTENTS
10
CONIC SECTIONS; MORE GRAPHING 937
10.1 The Circle and the Parabola 938
10.2 The Ellipse 952
10.3 The Hyperbola 962
10.4 Solving Nonlinear Systems of Equations 973
Chapter Summary and Review 981
Chapter Test 986
Group Project 988
11
MISCELLANEOUS TOPICS 989
11.1 The Binomial Theorem 990
11.2 Arithmetic Sequences and Series 1000
11.3 Geometric Sequences and Series 1011
Chapter Summary and Review 1024
Chapter Test 1028
Group Project 1029
Cumulative Review 1030
APPENDIXES APPENDIX 1: Roots and Powers A-1
APPENDIX 2: Answers to Selected Exercises A-3
INDEX I-1
PREFACE
Intermediate Algebra, Fourth Edition, is more than a simple upgrade of the third edition.
Substantial changes have been made to the example structure, the Study Sets, and the peda-
gogy. Throughout the process, the objective has been to ease teaching challenges and meet
students’educational needs.
Algebra, for many of today’s developmental math students, is like a foreign language.
They have difficulty translating the words, their meanings, and how they apply to problem
solving. With these needs in mind (and as educational research suggests), the fundamental
goal is to have students read, write, think, and speak using the language of algebra. Instruc-
tional approaches that include vocabulary, practice, and well-defined pedagogy, along with an
emphasis on reasoning, modeling, communication, and technology skills have been blended
to address this need.
The most common student question as they watch their instructors solve problems and as
they read the textbook is . . . Why?The new fourth edition addresses this question in a unique
way. Experience teaches us that it’s not enough to know how a problem is solved. Students
gain a deeper understanding of algebraic concepts if they know whya particular approach is
taken. This instructional truth was the motivation for adding aStrategyand Whyexplanation
to the solution of each worked example. The fourth edition now provides, on a consistent
basis, a concise answer to that all-important question: Why?
This is just one of several changes in this revision, and we trust that all of them will make
the course a better experience for both instructor and student.
NEW TO THIS EDITION
•
New Example Structure
•
New Chapter Opening Applications
•
New Study Skills Workshops
•
New Chapter Objectives
•
New Guided Practiceand Try It Yourselfsections in the Study Sets
•
New End-of-Chapter Organization
ix