TEXT CONTENTS

Preface xv

Application Index xxv

CHAPTER 1

REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 1

1.1 Tips for Success in Mathematics 2

1.2 Algebraic Expressions and Sets of Numbers 7

1.3 Operations on Real Numbers 17

Integrated Review-Algebraic Expressions

and Operations on Whole Numbers 28

1.4 Properties of Real Numbers 29

Chapter 1 Group Activity 40

Chapter 1 Vocabulary Check 40

Chapter 1 Highlights 41

Chapter 1 Review 43

Chapter 1 Test 45

CHAPTER 2

EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING 46

2.1 Linear Equations in One Variable 47

2.2 An Introduction to Problem Solving 56

2.3 Formulas and Problem Solving 68

2.4 Linear Inequalities and Problem Solving 76

Integrated Review-Linear Equations and Inequalities 87

2.5 Compound Inequalities 88

2.6 Absolute Value Equations 95

2.7 Absolute Value Inequalities 100

Chapter 2 Group Activity 106

Chapter 2 Vocabulary Check 107

Chapter 2 Highlights 108

Chapter 2 Review 113

Chapter 2 Test 115

Chapter 2 Cumulative Review 115

CHAPTER 3

GRAPHS AND FUNCTIONS 117

3.1 Graphing Equations 118

3.2 Introduction to Functions 129

3.3 Graphing Linear Functions 145

3.4 The Slope of a Line 154

3.5 Equations of Lines 166

Integrated Review-Linear Equations in Two Variables 176

3.6 Graphing Piecewise-Defined Functions and Shifting
and Reflecting Graphs of Functions 177

3.7 Graphing Linear Inequalities 186

Chapter 3 Group Activity 190

Chapter3 Vocabulary Check 191

Chapter 3 Highlights 191

Chapter 3 Review 197

Chapter 3 Test 200

Chapter 3 Cumulative Review 201

CHAPTER 4

SYSTEMS OF EQUATIONS 203

4.1 Solving Systems of Linear Equations in Two Variables 204

4.2 Solving Systems of Linear Equations in Three Variables 215

4.3 Systems of Linear Equations and Problem Solving 222

Integrated Review-Systems of Linear Equations 234

4.4 Solving Systems of Equations by Matrices 235

4.5 Systems of Linear Inequalities 242

Chapter 4 Group Activity 245

Chapter 4 Vocabulary Check 246

Chapter 4 Highlights 246

Chapter 4 Review 251

Chapter 4 Test 253

Chapter 4 Cumulative Review 253

CHAPTER 5

Exponents, Polynomials and Polynomial Functions 255

5.1 Exponents and Scientific Notation 256

5.2 More Work with Exponents and Scientific Notation 265

5.3 Polynomials and Polynomial Functions 271

5.4 Multiplying Polynomials 283

5.5 The Greatest Common Factor and Factoring by Grouping 292

5.6 Factoring Trinomials 297

5.7 Factoring by Special Products 306

Integrated Review-Operations on Polynomials
and Factoring Strategies 312

5.8 Solving Equations by Factoring and Problem Solving 316

Chapter 5 Group Activity 328

Chapter 5 Vocabulary Check 329

Chapter 5 Highlights 330

Chapter 5 Review 332

Chapter 5 Test 335

Chapter 5 Cumulative Review 336

CHAPTER 6

Rational Expressions 338

6.1 Rational Functions and Multiplying and Dividing
Rational Expressions 339

6.2 Adding and Subtracting Rational Expressions 351

6.3 Simplifying Complex Fractions 359

6.4 Dividing Polynomials: Long Division
and Synthetic Division 366

6.5 Solving Equations Containing Rational Expressions 376

Integrated Review-Expressions and Equations Containing
Rationol Expressions 383

6.6 Rational Equations and Problem Solving 385

6.7 Variation and Problem Solving 393

Chapter 6 Group Activity 401

Chapter 6 Vocabulary Check 402

Chapter 6 Highlights 403

Chapter 6 Review 406

Chapter 6 Test 409

Chapter 6 Cumulative Review 410

CHAPTER 7

RATIONAL EXPONENTS, RADICAlS, AND COMPLEX NUMBERS 412

7.1 Radicals and Radical Functions 413

7.2 Rational Exponents 421

7.3 Simplifying Radical Expressions 428

7.4 Adding, Subtracting, and Multiplying Radical Expressions 437

7.5 Rationalizing Denominators and Numerators
of Radical Expressions 443

Integrated Review-Radicals and Rational Exponents 449

7.6 Radical Equations and Problem Solving 450

7.7 Complex Numbers 460

Chapter 7 Group Activity 467

Chapter 7 Vocabulary Check 468

Chapter 7 Highlights 469

Chapter 7 Review 472

Chapter 7 Test 475

Chapter 7 Cumulative Review 476

CHAPTER 8

QUADRATIC EQUATIONS AND FUNCTIONS 479

8.1 Solving Quadratic Equations by Completing the Square 480

8.2 Solving Quadratic Equations by the Quadratic Formula 489

8.3 Solving Equations by Using Quadratic Methods 500

Integrated Review-Summary on Solving Quadratic Equations 508

8.4 Nonlinear Inequalities in One Variable 509

8.5 Quadratic Functions and Their Graphs 516

8.6 Further Graphing of Quadratic Functions 524

Chapter 8 Group Activity 531

Chapter 8 Vocabulary Check 532

Chapter 8 Highlights 533

Chapter 8 Review 536

Chapter 8 Test 537

Chapter 8 Cumulative Review 538

CHAPTER 9

EXPONENTIAL AND lOGARITHMIC fUNCTIONS 540

9.1 The Algebra of Functions; Composite Functions 541

9.2 Inverse Functions 547

9.3 Exponential Functions 557

9.4 Logarithmic Functions 565

9.5 Properties of Logarithms 573

Integrated Review-Functions and Properties of Logarithms 578

9.6 Common Logarithms, Natural Logarithms, and Change of Base 579

9.7 Exponential and Logarithmic Equations and Applications 585

Chapter 9 Group Activity 591

Chapter 9 Vocabulary Check 592

Chapter 9 Highlights 593

Chapter 9 Review 596

Chapter 9 Test 599

Chapter 9 Cumulative Review 600

CHAPTER 10

CONIC SECTIONS

10.1 The Parabola and the Circle 603

10.2 The Ellipse and the Hyperbola 612

Integrated Review-Graphing Conic Sections 619

10.3 Solving Nonlinear Systems of Equations 620

lO.4 Nonlinear Inequalities and Systems of Inequalities 625

Chapter 10 Group Activity 628

Chapter 10 Vocabulary Check 629

Chapter 10 Highlights 630

Chapter 10 Review 632

Chapter 10 Test 633

Chapter 10 Cumulative Review 634

CHAPTER 11

SEQUENCES, SERIES, AND THE BINOMIAL THEOREM 636

11.1 Sequences 637

11.2 Arithmetic and Geometric Sequences 641

11.3 Series 648

11A Partial Sums of Arithmetic and Geometric Sequences 653

11.5 The Binomial Theorem 660

Chapter 11 Group Activity 664

Chapter 11 Vocabulary Check 665

Chapter 11 Highlights 665

Chapter 11 Review 667

Chapter 11 Test 669

Chapter 11 Cumulative Review 670

APPENDICES 672

A THE BIGGER PICTURE/PRACTICE FINAL EXAM 672

B GEOMETRY 676

C STRETCHING AND COMPRESSING GRAPHS OF ABSOLUTE VALUE FUNCTIONS 683

D SOLVING SYSTEMS OF EQUATIONS USING DETERMINANTS 685

E AN INTRODUCTION TO USING A GRAPHING UTILITY 692

Answers to Selected Exercises Al

Graphing Answer Section G 1

Index II

Photo Credits P1

Course pages and outlines: Copyright © 2010 with all rights reserved by William V. Thayer