Contemporary Precalculus: A Graphing Approach

Hungerford approaches the subject of precalculus by integrating graphing technology into the course without losing sight of the fact that the underlying mathematics is the crucial issue. Mathematics is presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving.

Preface

ix

To the Instructor

xx

To the Student

xxiv

Basics

1

(58)

The Real Number System

2

(16)

Excursion: Decimal Representation of Real Numbers

15

(3)

Solving Equations Algebraically

18

(10)

Excursion: Absolute Value Equations

26

(2)

The Coordinate Plane

28

(10)

Lines

38

(21)

Chapter Review

51

(8)

Graphs and Technology

59

(58)

Graphs and Graphing Calculators

60

(13)

Solving Equations Graphically and Numerically

73

(7)

Applications of Equations

80

(11)

Optimization Applications

91

(5)

Linear Models

96

(21)

Chapter Review

109

(8)

Functions and Graphs

117

(88)

Functions

118

(9)

Functional Notation

127

(9)

Graphs of Functions

136

(14)

Graphs and Transformations

150

(15)

Excursion: Symmetry

159

(6)

Operations on Functions

165

(9)

Rates of Change

174

(12)

Inverse Functions

186

(19)

Chapter Review

195

(10)

Polynomial and Rational Functions

205

(100)

Quadratic Functions

206

(7)

Polynomial Functions

213

(11)

Excursion: Synthetic Division

221

(3)

Real Roots of Polynomials

224

(8)

Graphs of Polynomial Functions

232

(17)

Excursion: Polynomial Models

244

(5)

Rational Functions

249

(18)

Excursion: Other Rational Functions

263

(4)

Polynomial and Rational Inequalities

267

(14)

Excursion: Absolute Value Inequalities

278

(3)

Complex Numbers

281

(7)

Theory of Equations

288

(17)

Chapter Review

295

(10)

Exponential and Logarithmic Functions

305

(84)

Radicals and Rational Exponents

306

(14)

Excursion: Radical Equations

313

(7)

Exponential Functions

320

(20)

Excursion: Compound Interest and the Number e

334

(6)

Common and Natural Logarithmic Functions

340

(20)

Excursion: Logarithmic Functions to Other Bases

352

(8)

Algebraic Solutions of Exponential and Logarithmic Equations

360

(9)

Exponential, Logarithmic, and Other Models

369

(20)

Chapter Review

381

(8)

Trigonometric Functions

389

(76)

Angles and Their Measurement

390

(11)

The Sine, Cosine, and Tangent Functions

401

(8)

Algebra and Identities

409

(9)

Basic Graphs

418

(10)

Periodic Graphs and Simple Harmonic Motion

428

(19)

Excursion: Other Trigonometric Graphs

441

(6)

Other Trigonometric Functions

447

(18)

Chapter Review

456

(9)

Triangle Trigonometry

465

(42)

Right Triangle Trigonometry

466

(15)

The Law of Cosines

481

(7)

The Law of Sines

488

(19)

Chapter Review

501

(6)

Trigonometric Identities and Equations

507

(56)

Basic Identities and Proofs

508

(9)

Addition and Subtraction Identities

517

(13)

Excursion: Lines and Angles

526

(4)

Other Identities

530

(8)

Trigonometric Equations

538

(11)

Inverse Trigonometric Functions

549

(14)

Chapter Review

557

(6)

Applications of Trigonometry

563

(46)

The Complex Plane and Polar Form for Complex Numbers

564

(6)

DeMoivre's Theorem and nth Roots of Complex Numbers

570

(8)

Vectors in the Plane

578

(15)

The Dot Product

593

(16)

Chapter Review

603

(6)

Analytic Geometry

609

(72)

Plane Curves and Parametric Equations

610

(14)

Conic Sections

624

(14)

Translations and Rotations of Conics

638

(17)

Excursion: Rotation of Axes

649

(6)

Polar Coordinates

655

(9)

Polar Equations of Conics

664

(17)

Chapter Review

675

(6)

Systems of Equations

681

(50)

Systems of Linear Equations in Two Variables

682

(11)

Large Systems of Linear Equations

693

(15)

Matrix Methods for Square Systems

708

(11)

Systems of Nonlinear Equations

719

(12)

Chapter Review

726

(5)

Discrete Algebra

731

(48)

Sequences and Sums

732

(10)

Arithmetic Sequences

742

(5)

Geometric Sequences

747

(10)

Excursion: Infinite Series

752

(5)

The Binomial Theorem

757

(7)

Mathematical Induction

764

(15)

Chapter Review

774

(5)

Algebra Review Appendix

779

(18)

Geometry Review Appendix

797

(6)

Program Appendix

803

(4)

Answers to Odd-Numbered Exercises

807

Index of Applications

1

(4)

Index

5

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Contemporary Precalculus: A Graphing Approach

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