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Tables of Contents for College Algebra

Chapter/Section Title

Page #

Page Count

PREFACE

XIII

CHAPTER 1 MODELING AND PROBLEM SOLVING

1

28

1-1 A Case for Algebra

1

6

Algebra Is an Analytical Tool

4

1

Algebra Is Rich in Concepts and Contexts

4

1

Algebra Is Part of Our Intellectual Heritage

5

1

You May Actually Use Algebra!

5

1

Some Suggestions for Feeling at Home with This Book

5

2

1-2 Models of Quantitative Relationships

7

12

Three Types of Model

7

1

Information Provided by the Three Types of Model

8

1

Creating One Model from Another

9

10

1-3 Problem-Solving Strategies

19

8

First Step: Understand the Problem

20

1

Second Step: Devise a Plan

21

1

Third Step: Carry Out the Plan

22

1

Fourth Step: Look Back

23

4

Chapter Review

27

2

CHAPTER 2 FUNCTIONS

29

44

2-1 Three Views of Functions

29

11

The Definition of Function

29

2

A Numerical View of Functions

31

1

An Analytical View of Functions

32

1

A Graphical View of Functions

33

3

Reasons to Study Functions and Their Models

36

4

2-2 The Concept of Function As Process

40

11

Functional Notation

41

1

Combining Functions

42

9

2-3 Domain and Range

51

14

Domain and Range of Abstract Functions

52

3

Domain and Range of Functions in a Physical Context

55

2

Sequences

57

2

Dynamic Behavior: Increasing and Decreasing Functions

59

6

2-4 Solving Equations and Inequalities Graphically

65

6

Solving Equations Graphically

66

2

Solving Inequalities Graphically

68

3

Chapter Review

71

2

CHAPTER 3 LINEAR FUNCTIONS

73

42

3-1 Three Views of Linear Functions

73

10

A Numerical View of Linear Functions

73

4

A Graphical View of Linear Functions

77

1

An Analytical View of Linear Functions

78

2

Summary

80

3

3-2 Modeling and Problem Solving with Linear Functions

83

8

Modeling of Linear Relationships

83

2

Linear Variation

85

1

Arithmetic Sequences

86

5

3-3 Linear Modeling of Nonlinear Relationships

91

10

Linearization

91

2

Average Rate of Change

93

8

3-4 Piecewise Linear Functions

101

12

Three Views of Piecewise Linear Functions

102

2

Three Views of Linear Absolute Value Functions

104

5

Solving Linear Absolute Value Inequalities

109

4

Chapter Review

113

2

CHAPTER 4 LINEAR SYSTEMS

115

34

4-1 Systems of Linear Equations

115

10

Methods of Solving 2 X 2 Systems

115

2

Methods of Solving 3 X 3 Systems

117

2

Numbers of Solutions to 2 X 2 and 3 X 3 Systems

119

6

4-2 Matrix Solutions of Systems of Linear Equations

125

14

Augmented Matrix of a System

125

1

Matrix Row Operations

126

2

Gauss-Jordan Elimination

128

2

Reduced Row-Echelon Matrices

130

1

Matrices and Numbers of Solutions

131

5

Summary: Matrix Versus Nonmatrix Methods

136

3

4-3 Systems of Linear Inequalities and Linear Programming

139

8

Graphs of Linear Inequalities in Two Variables

139

2

Graphs of Systems of Linear Inequalities in Two Variables

141

1

Linear Programming

142

5

Chapter Review

147

2

CHAPTER 5 QUADRATIC FUNCTIONS

149

28

5-1 Three Views of Quadratic Functions

149

17

A Graphical View of Quadratic Functions

150

4

An Analytical View of Quadratic Functions

154

6

A Numerical View of Quadratic Functions

160

6

5-2 Modeling and Problem Solving with Quadratic Functions

166

9

Optimization Problems

166

2

Solving Quadratic Inequalities

168

2

Fitting a Quadratic Function to a Table

170

5

Chapter Review

175

2

CHAPTER 6 QUADRATIC RELATIONS

177

74

6-1 Relations

177

10

Three Views of Relations

179

5

Implicit Functions

184

3

6-2 A Graphical View of Conic Sections

187

15

A Graphical View of Parabolas

189

1

A Graphical View of Ellipses

190

5

A Graphical View of Hyperbolas

195

5

Exceptional Graphs

200

2

6-3 Graphical Transformations

202

15

Stretches and Compressions

203

2

Shifts

205

1

Reflections

206

2

Applying a Sequence of Transformations

208

3

Summary

211

6

6-4 An Analytical View of Conic Sections

217

15

An Analytical View of Parabolas

217

4

An Analytical View of Ellipses

221

4

An Analytical View of Hyperbolas

225

7

6-5 Square Root Functions

232

6

6-6 Systems of Quadratic Equations and Inequalities

238

11

Solving Systems of Quadratic Equations Analytically

239

2

Solving Systems of Quadratic Equations Graphically

241

2

Solving Systems of Quadratic Inequalities

243

6

Chapter Review

249

2

CHAPTER 7 POLYNOMIAL FUNCTIONS

251

44

7-1 Power Functions

251

8

Basic Power Functions and Their Graphs

251

2

Graphical Transformations

253

1

Polynomial Variation

254

5

7-2 An Analytical View of Polynomial Functions

259

8

Factors and Zeros

260

2

The Fundamental Theorem of Algebra

262

5

7-3 A Graphical View of Polynomial Functions

267

14

Points of Interest

268

5

End Behavior

273

3

Symmetry

276

5

7-4 A Numerical View of Polynomial Functions

281

6

nth-Order Differences

281

1

Fitting a Polynomial Function to a Table

282

1

A Numerical Method for Finding Zeros

283

2

A Comparison of Methods for Finding Zeros

285

2

7-5 Solving Polynomial Inequalities

287

6

Solving Polynomial Inequalities Graphically

287

2

Solving Polynomial Inequalities Analytically

289

4

Chapter Review

293

2

CHAPTER 8 RATIONAL FUNCTIONS

295

28

8-1 Reciprocal Power Functions

295

5

Three Views of Reciprocal Power Functions

296

2

Inverse Variation

298

2

Graphical Transformations

300

4

8-2 Discontinuities and End Behavior of Rational Functions

304

10

Discontinuities and Vertical Asymptotes

305

3

End Behavior and Horizontal Asymptotes

308

6

8-3 Solving Rational Inequalities

314

6

A Graphical Method

316

1

The Test-Value Method

316

1

The Scan Method

317

3

Chapter Review

320

3

CHAPTER 9 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

323

9-1 Exponential Functions

323

15

A Numerical View of Exponential Functions

324

2

An Analytical View of Exponential Functions

326

3

A Graphical View of Exponential Functions

329

3

Geometric Sequences and Series

332

6

9-2 The Special Number e

338

7

The Definition of e

338

3

Using the Base e to Express Exponential Functions

341

4

9-3 Inverse Functions

345

13

One-to-One Functions

346

2

Finding Inverses of One-to-One Functions

348

10

9-4 Logarithmic Functions

358

16

A Numerical View of Logarithmic Functions

360

3

A Graphical View of Logarithmic Functions

363

2

An Analytical View of Logarithmic Functions

365

9

9-5 Curve Fitting

374

14

Fitting Linear Functions to Data

375

3

Fitting Logarithmic Functions to Data

378

2

Fitting Exponential Functions to Data

380

1

Fitting Power Functions to Data

381

2

Curve Fitting on Your Calculator

383

5

Chapter Review

388

APPENDIX A BASIC ALGEBRA REFERENCE

A1

A-1 Accuracy and Precision

A1

A-2 Linear Equations

A4

A-3 The Coordinate Plane

A5

A-4 The Pythagorean Theorem and the Distance Formula

A7

A-5 Basic Graphing Techniques

A8

A-6 Graphing Linear Equations

A11

A-7 Intervals

A15

A-8 Linear Inequalities

A17

A-9 Absolute Value Equations and Inequalities

A19

A-10 Systems of Linear Equations

A22

A-11 The Laws of Exponents

A26

A-12 Factoring

A28

A-13 Quadratic Equations

A32

A-14 Operations with Complex Numbers

A36

A-15 Division and Synthetic Division of Polynomials

A38

A-16 Algebraic Fractions

A41

A-17 Equations with Algebraic Fractions

A48

A-18 Radicals and Rational Exponents

A49

A-19 Equations with Radicals

A54

APPENDIX B TIPS FOR GRAPHING FUNCTIONS WITH A CALCULATOR

B1

B-1 The Viewing Window

B1

B-2 Graphing Linear Functions

B6

B-3 Graphing Quadratic Functions

B7

B-4 Graphing Quadratic Relations

B9

B-5 Graphing Polynomial Functions

B11

B-6 Graphing Rational Functions

B14

ANSWERS TO ODD-NUMBERED EXERCISES

ANS 1

INDEX

11