PrecalculusGraphical, Numerical, Algebraic

Franklin D. Demana The Ohio State University

Bert K. Waits The Ohio State University

Gregory D. Foley Liberal Arts and Science Academyof Austin

Daniel Kennedy Baylor School

*AP is a registered trademark of the College Board, which was not involved in the production of, and doesnot endorse, this product.

S E V E N T H E D I T I O N

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Library of Congress Cataloging-in-Publication Data

Precalculus : graphical, numerical, algebraic / Franklin Demana … [et al.].—7th ed.p. cm.

ISBN 0-321-35693-4 (student edition)1. Algebra--Textbook. 2. Trigonometry--Textbooks. I. Demana, Franklin D., 1938-

QA154.3.P74 2006512'.13--dc22

2005051543

Copyright © 2007 Pearson Education, Inc. All rights reserved. No part of this publication may bereproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording, or otherwise, without the prior written permission of thepublisher. Printed in the United States of America. For information on obtaining permission for useof material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 75 Arlington Street, Suite 300, Boston, MA 02116, fax your request to 617-848-7047, or e-mail at http://www.pearsoned.com/legal/permissions.htm.

1 2 3 4 5 6 7 8 9 10—QWT—10 09 08 07 06

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Contents

CHAPTER P Prerequisites 1

P.1 Real Numbers 1

Representing Real Numbers ~ Order and Interval Notation ~ BasicProperties of Algebra ~ Integer Exponents ~ Scientific Notation

P.2 Cartesian Coordinate System 14

Cartesian Plane ~ Absolute Value of a Real Number ~ DistanceFormulas ~ Midpoint Formulas ~ Equations of Circles ~Applications

P.3 Linear Equations and Inequalities 24

Equations ~ Solving Equations ~ Linear Equations in One Variable ~Linear Inequalities in One Variable

P.4 Lines in the Plane 31

Slope of a Line ~ Point-Slope Form Equation of a Line ~ Slope-Intercept Form Equation of a Line ~ Graphing Linear Equations inTwo Variables ~ Parallel and Perpendicular Lines ~ Applying LinearEquations in Two Variables

P.5 Solving Equations Graphically, Numerically, and Algebraically 44

Solving Equations Graphically ~ Solving Quadratic Equations ~Approximating Solutions of Equations Graphically ~ ApproximatingSolutions of Equations Numerically with Tables ~ Solving Equationsby Finding Intersections

P.6 Complex Numbers 53

Complex Numbers ~ Operations with Complex Numbers ~ ComplexConjugates and Division ~ Complex Solutions of QuadraticEquations

P.7 Solving Inequalities Algebraically and Graphically 59

Solving Absolute Value Inequalities ~ Solving Quadratic Inequalities~ Approximating Solutions to Inequalities ~ Projectile Motion

Key Ideas 65

Review Exercises 66

CHAPTER 1 Functions and Graphs 69

1.1 Modeling and Equation Solving 70

Numerical Models ~ Algebraic Models ~ Graphical Models ~The Zero Factor Property ~ Problem Solving ~ Grapher Failure and Hidden Behavior ~ A Word About Proof

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1.2 Functions and Their Properties 86

Function Definition and Notation ~ Domain and Range ~ Continuity~ Increasing and Decreasing Functions ~ Boundedness ~ Local andAbsolute Extrema ~ Symmetry ~ Asymptotes ~ End Behavior

1.3 Twelve Basic Functions 106

What Graphs Can Tell Us ~ Twelve Basic Functions ~ AnalyzingFunctions Graphically

1.4 Building Functions from Functions 117

Combining Functions Algebraically ~ Composition of Functions ~Relations and Implicitly Defined Functions

1.5 Parametric Relations and Inverses 127

Relations Defined Parametrically ~ Inverse Relations and InverseFunctions

1.6 Graphical Transformations 138

Transformations ~ Vertical and Horizontal Translations ~Reflections Across Axes ~ Vertical and Horizontal Stretches andShrinks ~ Combining Transformations

1.7 Modeling With Functions 151

Functions from Formulas ~ Functions from Graphs ~ Functions from Verbal Descriptions ~ Functions from Data

Math at Work 164

Key Ideas 164

Review Exercises 165

Chapter Project 168

CHAPTER 2 Polynomial, Power, and Rational Functions 169

2.1 Linear and Quadratic Functions and Modeling 170

Polynomial Functions ~ Linear Functions and Their Graphs ~Average Rate of Change ~ Linear Correlation and Modeling ~Quadratic Functions and Their Graphs ~ Applications of QuadraticFunctions

2.2 Power Functions with Modeling 188

Power Functions and Variation ~ Monomial Functions and TheirGraphs ~ Graphs of Power Functions ~ Modeling with PowerFunctions

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2.3 Polynomial Functions of Higher Degree with Modeling 200

Graphs of Polynomial Functions ~ End Behavior of PolynomialFunctions ~ Zeros of Polynomial Functions ~ Intermediate ValueTheorem ~ Modeling

2.4 Real Zeros of Polynomial Functions 214

Long Division and the Division Algorithm ~ Remainder and FactorTheorems ~ Synthetic Division ~ Rational Zeros Theorem ~ Upperand Lower Bounds

2.5 Complex Zeros and the Fundamental Theorem of Algebra 228

Two Major Theorems ~ Complex Conjugate Zeros ~ Factoring withReal Number Coefficients

2.6 Graphs of Rational Functions 237

Rational Functions ~ Transformations of the Reciprocal Function ~Limits and Asymptotes ~ Analyzing Graphs of Rational Functions ~Exploring Relative Humidity

2.7 Solving Equations in One Variable 248

Solving Rational Equations ~ Extraneous Solutions ~ Applications

2.8 Solving Inequalities in One Variable 257

Polynomial Inequalities ~ Rational Inequalities ~ Other Inequalities~ Applications

Math at Work 267

Key Ideas 268

Review Exercises 269

Chapter Project 273

CHAPTER 3 Exponential, Logistic, and Logarithmic Functions 275

3.1 Exponential and Logistic Functions 276

Exponential Functions and Their Graphs ~ The Natural Base e ~Logistic Functions and Their Graphs ~ Population Models

3.2 Exponential and Logistic Modeling 290

Constant Percentage Rate and Exponential Functions ~ ExponentialGrowth and Decay Models ~ Using Regression to Model Population~ Other Logistic Models

3.3 Logarithmic Functions and Their Graphs 300

Inverses of Exponential Functions ~ Common Logarithms—Base 10~ Natural Logarithms—Base e ~ Graphs of Logarithmic Functions ~Measuring Sound Using Decibels

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3.4 Properties of Logarithmic Functions 310

Properties of Logarithms ~ Change of Base ~ Graphs of LogarithmicFunctions with Base b ~ Re-expressing Data

3.5 Equation Solving and Modeling 320

Solving Exponential Equations ~ Solving Logarithmic Equations ~Orders of Magnitude and Logarithmic Models ~ Newton’s Law ofCooling ~ Logarithmic Re-expression

3.6 Mathematics of Finance 334

Interest Compounded Annually ~ Interest Compounded k Times perYear ~ Interest Compounded Continuously ~ Annual PercentageYield ~ Annuities—Future Value ~ Loans and Mortgages—PresentValue

Key Ideas 344

Review Exercises 344

Chapter Project 348

CHAPTER 4 Trigonometric Functions 349

4.1 Angles and Their Measures 350

The Problem of Angular Measure ~ Degrees and Radians ~ CircularArc Length ~ Angular and Linear Motion

4.2 Trigonometric Functions of Acute Angles 360

Right Triangle Trigonometry ~ Two Famous Triangles ~ EvaluatingTrigonometric Functions with a Calculator ~ Common CalculatorErrors When Evaluating Trig Functions ~ Applications of RightTriangle Trigonometry

4.3 Trigonometry Extended: The Circular Functions 370

Trigonometric Functions of Any Angle ~ Trigonometric Functions ofReal Numbers ~ Periodic Functions ~ The 16-Point Unit Circle

4.4 Graphs of Sine and Cosine: Sinusoids 384

The Basic Waves Revisited ~ Sinusoids and Transformations ~Modeling Periodic Behavior with Sinusoids

4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 396

The Tangent Function ~ The Cotangent Function ~ The SecantFunction ~ The Cosecant Function

4.6 Graphs of Composite Trigonometric Functions 406

Combining Trigonometric and Algebraic Functions ~ Sums andDifferences of Sinusoids ~ Damped Oscillation

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4.7 Inverse Trigonometric Functions 414

Inverse Sine Function ~ Inverse Cosine and Tangent Functions ~Composing Trigonometric and Inverse Trigonometric Functions ~Applications of Inverse Trigonometric Functions

4.8 Solving Problems with Trigonometry 425

More Right Triangle Problems ~ Simple Harmonic Motion

Key Ideas 438

Review Exercises 439

Chapter Project 442

CHAPTER 5 Analytic Trigonometry 443

5.1 Fundamental Identities 444

Identities ~ Basic Trigonometric Identities ~ Pythagorean Identities~ Cofunction Identities ~ Odd-Even Identities ~ SimplifyingTrigonometric Expressions ~ Solving Trigonometric Equations

5.2 Proving Trigonometric Identities 454

A Proof Strategy ~ Proving Identities ~ Disproving Non-Identities ~Identities in Calculus

5.3 Sum and Difference Identities 463

Cosine of a Difference ~ Cosine of a Sum ~ Sine of a Difference orSum ~ Tangent of a Difference or Sum ~ Verifying a SinusoidAlgebraically

5.4 Multiple-Angle Identities 471

Double-Angle Identities ~ Power-Reducing Identities ~ Half-AngleIdentities ~ Solving Trigonometric Equations

5.5 The Law of Sines 478

Deriving the Law of Sines ~ Solving Triangles (AAS, ASA) ~ TheAmbiguous Case (SSA) ~ Applications

5.6 The Law of Cosines 487

Deriving the Law of Cosines ~ Solving Triangles (SAS, SSS) ~Triangle Area and Heron’s Formula ~ Applications

Math at Work 496

Key Ideas 497

Review Exercises 497

Chapter Project 500

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CHAPTER 6 Applications of Trigonometry 501

6.1 Vectors in the Plane 502

Two-Dimensional Vectors ~ Vector Operations ~ Unit Vectors ~Direction Angles ~ Applications of Vectors

6.2 Dot Product of Vectors 514

The Dot Product ~ Angle Between Vectors ~ Projecting One Vectoronto Another ~ Work

6.3 Parametric Equations and Motion 522

Parametric Equations ~ Parametric Curves ~ Eliminating theParameter ~ Lines and Line Segments ~ Simulating Motion with aGrapher

6.4 Polar Coordinates 534

Polar Coordinate System ~ Coordinate Conversion ~ EquationConversion ~ Finding Distance Using Polar Coordinates

6.5 Graphs of Polar Equations 541

Polar Curves and Parametric Curves ~ Symmetry ~ Analyzing PolarGraphs ~ Rose Curves ~ Limaçon Curves ~ Other Polar Curves

6.6 De Moivre’s Theorem and nth Roots 550

The Complex Plane ~ Trigonometric Form of Complex Numbers ~Multiplication and Division of Complex Numbers ~ Powers ofComplex Numbers ~ Roots of Complex Numbers

Key Ideas 561

Review Exercises 562

Chapter Project 565

CHAPTER 7 Systems and Matrices 567

7.1 Solving Systems of Two Equations 568

The Method of Substitution ~ Solving Systems Graphically ~The Method of Elimination ~ Applications

7.2 Matrix Algebra 579

Matrices ~ Matrix Addition and Subtraction ~ Matrix Multiplication~ Identity and Inverse Matrices ~ Determinant of a Square Matrix ~Applications

7.3 Multivariate Linear Systems and Row Operations 594

Triangular Form for Linear Systems ~ Gaussian Elimination ~Elementary Row Operations and Row Echelon Form ~ ReducedRow Echelon Form ~ Solving Systems with Inverse Matrices ~Applications

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7.4 Partial Fractions 608

Partial Fraction Decomposition ~ Denominators with Linear Factors~ Denominators with Irreducible Quadratic Factors ~ Applications

7.5 Systems of Inequalities in Two Variables 617

Graph of an Inequality ~ Systems of Inequalities ~ LinearProgramming

Math at Work 625

Key Ideas 626

Review Exercises 626

Chapter Project 630

CHAPTER 8 Analytic Geometry in Two and Three Dimensions 631

8.1 Conic Sections and Parabolas 632

Conic Sections ~ Geometry of a Parabola ~ Translations ofParabolas ~ Reflective Property of a Parabola

8.2 Ellipses 644

Geometry of an Ellipse ~ Translations of Ellipses ~ Orbits andEccentricity ~ Reflective Property of an Ellipse

8.3 Hyperbolas 656

Geometry of a Hyperbola ~ Translations of Hyperbolas ~Eccentricity and Orbits ~ Reflective Property of a Hyperbola ~Long-Range Navigation

8.4 Translation and Rotation of Axes 666

Second-Degree Equations in Two Variables ~ Translating Axes versus Translating Graphs ~ Rotation of Axes ~ Discriminant Test

8.5 Polar Equations of Conics 675

Eccentricity Revisited ~ Writing Polar Equations for Conics ~Analyzing Polar Equations of Conics ~ Orbits Revisited

8.6 Three-Dimensional Cartesian Coordinate System 685

Three-Dimensional Cartesian Coordinates ~ Distance and MidpointFormulas ~ Equation of a Sphere ~ Planes and Other Surfaces ~Vectors in Space ~ Lines in Space

Key Ideas 695

Review Exercises 696

Chapter Project 698

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CHAPTER 9 Discrete Mathematics 699

9.1 Basic Combinatorics 700

Discrete Versus Continuous ~ The Importance of Counting ~ TheMultiplication Principle of Counting ~ Permutations ~ Combinations~ Subsets of an n-Set

9.2 The Binomial Theorem 711

Powers of Binomials ~ Pascal’s Triangle ~ The Binomial Theorem ~Factorial Identities

9.3 Probability 718

Sample Spaces and Probability Functions ~ DeterminingProbabilities ~ Venn Diagrams and Tree Diagrams ~ ConditionalProbability ~ Binomial Distributions

9.4 Sequences 732

Infinite Sequences ~ Limits of Infinite Sequences ~ Arithmetic andGeometric Sequences ~ Sequences and Graphing Calculators

9.5 Series 742

Summation Notation ~ Sums of Arithmetic and GeometricSequences ~ Infinite Series ~ Convergence of Geometric Series

9.6 Mathematical Induction 752

The Tower of Hanoi Problem ~ Principle of Mathematical Induction~ Induction and Deduction

9.7 Statistics and Data (Graphical) 759

Statistics ~ Displaying Categorical Data ~ Stemplots ~ FrequencyTables ~ Histograms ~ Time Plots

9.8 Statistics and Data (Algebraic) 771

Parameters and Statistics ~ Mean, Median, and Mode ~ The Five-Number Summary ~ Boxplots ~ Variance and Standard Deviation ~Normal Distributions

Math at Work 785

Key Ideas 786

Review Exercises 786

Chapter Project 790

CHAPTER 10 An Introduction to Calculus: Limits, Derivatives, and Integrals 791

10.1 Limits and Motion: The Tangent Problem 792

Average Velocity ~ Instantaneous Velocity ~ Limits Revisited ~The Connection to Tangent Lines ~ The Derivative

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Contents xi

10.2 Limits and Motion: The Area Problem 804

Distance from a Constant Velocity ~ Distance from a ChangingVelocity ~ Limits at Infinity ~ The Connection to Areas ~ TheDefinite Integral

10.3 More on Limits 813

A Little History ~ Defining a Limit Informally ~ Properties of Limits~ Limits of Continuous Functions ~ One-sided and Two-sided Limits~ Limits Involving Infinity

10.4 Numerical Derivatives and Integrals 828

Derivatives on a Calculator ~ Definite Integrals on a Calculator ~Computing a Derivative from Data ~ Computing a Definite Integralfrom Data

Key Ideas 836

Review Exercises 836

Chapter Project 838

APPENDIX A Algebra Review

A.1 Radicals and Rational Exponents 839

Radicals ~ Simplifying Radical Expressions ~ Rationalizing theDenominator ~ Rational Exponents

A.2 Polynomials and Factoring 845

Adding, Subtracting, and Multiplying Polynomials ~ SpecialProducts ~ Factoring Polynomials Using Special Products ~Factoring Trinomials ~ Factoring by Grouping

A.3 Fractional Expressions 852

Domain of an Algebraic Expression ~ Reducing RationalExpressions ~ Operations with Rational Expressions ~ CompoundRational Expressions

APPENDIX B Key Formulas

B.1 Formulas from Algebra 857

Exponents ~ Radicals and Rational Expressions ~ Special Products~ Factoring Polynomials ~ Inequalities ~ Quadratic Formula ~Logarithms ~ Determinants ~ Arithmetic Sequences and Series ~Geometric Sequences and Series ~ Factorial ~ Binomial Coefficient~ Binomial Theorem

B.2 Formulas from Geometry 858

Triangle ~ Trapezoid ~ Circle ~ Sector of Circle ~ Right CircularCone ~ Right Circular Cylinder ~ Right Triangle ~ Parallelogram ~Circular Ring ~ Ellipse ~ Cone ~ Sphere

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B.3 Formulas from Trigonometry 859

Angular Measure ~ Reciprocal Identities ~ Quotient Identities ~Pythagorean Identities ~ Odd-Even Identities ~ Sum and DifferenceIdentities ~ Cofunction Identities ~ Double-Angle Identities ~Power-Reducing Identities ~ Half-Angle Identities ~ Triangles ~Trigonometric Form of a Complex Number ~ De Moivre’s Theorem

B.4 Formulas from Analytic Geometry 860

Basic Formulas ~ Equations of a Line ~ Equation of a Circle ~Parabolas with Vertex (h, k) ~ Ellipses with Center (h, k) and a > b > 0 ~ Hyperbolas with Center (h, k)

B.5 Gallery of Basic Functions 862

APPENDIX C Logic

C.1 Logic: An Introduction 863

Statements ~ Compound Statements

C.2 Conditionals and Biconditionals 869

Forms of Statements ~ Valid Reasoning

Glossary 877

Selected Answers 895

Applications Index 1015

Index 1019

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About the Authors

Franklin D. DemanaFrank Demana received his master’s degree in mathematics and his Ph.D. from Michigan State University. Currently, he is Professor Emeritus ofMathematics at The Ohio State University. As an active supporter of the use of technology to teach and learn mathematics, he is cofounder of thenational Teachers Teaching with Technology (T3) professional development program. He has been the director and codirector of more than $10 mil-lion of National Science Foundation (NSF) and foundational grant activities. He is currently a co–principal investigator on a $3 million grant fromthe U.S. Department of Education Mathematics and Science Educational Research program awarded to The Ohio State University. Along with fre-quent presentations at professional meetings, he has published a variety of articles in the areas of computer- and calculator-enhanced mathematicsinstruction. Dr. Demana is also cofounder (with Bert Waits) of the annual International Conference on Technology in Collegiate Mathematics(ICTCM). He is co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics,and co-recipient of the 1998 Christofferson-Fawcett Mathematics Education Award presented by the Ohio Council of Teachers of Mathematics.

Dr. Demana coauthored Calculus: Graphical, Numerical, Algebraic; Essential Algebra: A Calculator Approach; Transition to CollegeMathematics; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; Precalculus: Functions andGraphs; and Intermediate Algebra: A Graphing Approach.

Bert K. WaitsBert Waits received his Ph.D. from The Ohio State University and is currently Professor Emeritus of Mathematics there. Dr. Waits is cofounder ofthe national Teachers Teaching with Technology (T3) professional development program, and has been codirector or principal investigator on sev-eral large National Science Foundation projects. Dr. Waits has published articles in more than 50 nationally recognized professional journals. He fre-quently gives invited lectures, workshops, and minicourses at national meetings of the MAA and the National Council of Teachers of Mathematics(NCTM) on how to use computer technology to enhance the teaching and learning of mathematics. He has given invited presentations at theInternational Congress on Mathematical Education (ICME-6, -7, and -8) in Budapest (1988), Quebec (1992), and Seville (1996). Dr. Waits is co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics, and is thecofounder (with Frank Demana) of the ICTCM. He is also co-recipient of the 1998 Christofferson-Fawcett Mathematics Education Award present-ed by the Ohio Council of Teachers of Mathematics.

Dr. Waits coauthored Calculus: Graphical, Numerical, Algebraic; College Algebra and Trigonometry: A Graphing Approach; College Algebra: AGraphing Approach; Precalculus: Functions and Graphs; and Intermediate Algebra: A Graphing Approach.

Gregory D. FoleyGreg Foley received B.A. and M.A. degrees in mathematics and a Ph.D. in mathematics education from The University of Texas at Austin. He is Directorof the Liberal Arts and Science Academy of Austin, the advanced academic magnet high school program of the Austin Independent School District inTexas. Dr. Foley has taught elementary arithmetic through graduate-level mathematics, as well as upper division and graduate-level mathematics educa-tion classes. From 1977 to 2004, he held full time faculty positions at North Harris County College, Austin Community College, The Ohio StateUniversity, Sam Houston State University, and Appalachian State University, where he was Distinguished Professor of Mathematics Education in theDepartment of Mathematical Sciences and directed the Mathematics Education Leadership Training (MELT) program. Dr. Foley has presented over 200lectures, workshops, and institutes throughout the United States and internationally, has directed a variety of funded projects, and has published articlesin several professional journals. Active in various learned societies, he is a member of the Committee on the Mathematical Education of Teachers of theMathematical Association of America (MAA). In 1998, Dr. Foley received the biennial American Mathematical Association of Two-Year Colleges(AMATYC) Award for Mathematics Excellence and in 2005, he received the annual Teachers Teaching with Technology (T3) Leadership Award.

Daniel KennedyDan Kennedy received his undergraduate degree from the College of the Holy Cross and his master’s degree and Ph.D. in mathematics from the Universityof North Carolina at Chapel Hill. Since 1973 he has taught mathematics at the Baylor School in Chattanooga, Tennessee, where he holds the Cartter LuptonDistinguished Professorship. Dr. Kennedy became an Advanced Placement Calculus reader in 1978, which led to an increasing level of involvement withthe program as workshop consultant, table leader, and exam leader. He joined the Advanced Placement Calculus Test Development Committee in 1986,then in 1990 became the first high school teacher in 35 years to chair that committee. It was during his tenure as chair that the program moved to requiregraphing calculators and laid the early groundwork for the 1998 reform of the Advanced Placement Calculus curriculum. The author of the 1997 Teacher’sGuide––AP* Calculus, Dr. Kennedy has conducted more than 50 workshops and institutes for high school calculus teachers. His articles on mathematicsteaching have appeared in the Mathematics Teacher and the American Mathematical Monthly, and he is a frequent speaker on education reform at pro-fessional and civic meetings. Dr. Kennedy was named a Tandy Technology Scholar in 1992 and a Presidential Award winner in 1995.

Dr. Kennedy coauthored Calculus: Graphical, Numerical, Algebraic; Prentice Hall Algebra I; Prentice Hall Geometry; and Prentice Hall Algebra 2.

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PrefaceAlthough much attention has been paid since 1990 to reforming calculus courses, precal-culus textbooks have remained surprisingly traditional. With this edition of Precalculus:Graphical, Numerical, Algebraic the authors have designed such a precalculus course. Forthose students continuing on in a calculus course, this precalculus textbook concludes witha chapter that prepares students for the two central themes of calculus: instantaneous rateof change and continuous accumulation. This intuitively appealing preview of calculus isboth more useful and more reasonable than the traditional, unmotivated foray into thecomputation of limits.

Recognizing that precalculus could be a capstone course for many students, the authorsalso include quantitative literacy topics such as probability, statistics, and the mathemat-ics of finance. Their goal is to provide students with the good critical-thinking skills need-ed to succeed in any endeavor.

Continuing in the spirit of two earlier editions, the authors have integrated graphing tech-nology throughout the course, not as an additional topic but as an essential tool for bothmathematical discovery and effective problem solving. Graphing technology enables stu-dents to study a full catalog of basic functions at the beginning of the course, thereby giv-ing them insights into function properties that are not seen in many books until later chap-ters. By connecting the algebra of functions to the visualization of their graphs, the authorsare even able to introduce students to parametric equations, piecewise-defined functions,limit notation, and an intuitive understanding of continuity as early as Chapter 1.

Once students are comfortable with the language of functions, the authors guide themthrough a more traditional exploration of twelve basic functions and their algebraic prop-erties, always reinforcing the connections among their algebraic, graphical, and numericalrepresentations. The book uses a consistent approach to modeling, emphasizing in everychapter the use of particular types of functions to model behavior in the real world.

Our Approach

The Rule of Four—A Balanced ApproachA principal feature of this edition is the balance among the algebraic, numerical, graphi-cal, and verbal methods of representing problems: the rule of four. For instance, we obtainsolutions algebraically when that is the most appropriate technique to use, and we obtainsolutions graphically or numerically when algebra is difficult to use. We urge students tosolve problems by one method and then support or confirm their solutions by using anothermethod. We believe that students must learn the value of each of these methods or represen-tations and must learn to choose the one most appropriate for solving the particular problemunder consideration. This approach reinforces the idea that to understand a problem fully,students need to understand it algebraically as well as graphically and numerically.

Problem-Solving ApproachSystematic problem solving is emphasized in the examples throughout the text, using thefollowing variation of Polya’s problem-solving process:

• understand the problem,

• develop a mathematical model,

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*AP is a registered trademark of the College Board, which was not involved in the production of, and doesnot endorse, this product.

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xiv

• solve the mathematical model and support or confirm the solutions, and

• interpret the solution.

Students are encouraged to use this process throughout the text.

Twelve Basic FunctionsTwelve Basic Functions are emphasized throughout the book as a major theme and focus.These functions are:

• The Identity Function

• The Squaring Function

• The Cubing Function

• The Reciprocal Function

• The Square Root Function

• The Exponential Function

• The Natural Logarithm Function

• The Sine Function

• The Cosine Function

• The Absolute Value Function

• The Greatest Integer Function

• The Logistic Function

One of the most distinctive features of this textbook is that it introduces students to the fullvocabulary of functions early in the course. Students meet the twelve basic functionsgraphically in Chapter 1 and are able to compare and contrast them as they learn aboutconcepts like domain, range, symmetry, continuity, end behavior, asymptotes, extrema,and even periodicity—concepts that are difficult to appreciate when the only examples ateacher can refer to are polynomials. With this book, students are able to characterize func-tions by their behavior within the first few weeks of classes. (For example, thanks to graph-ing technology, it is no longer necessary to understand radians before one can learn thatthe sine function is bounded, periodic, odd, and continuous, with domain (–�, �) andrange [–1, 1].) Once students have a comfortable understanding of functions in general, therest of the course consists of studying the various types of functions in greater depth, par-ticularly with respect to their algebraic properties and modeling applications.

These functions are used to develop the fundamental analysis skills that are needed in cal-culus and advanced mathematics courses. Section 1.2 provides an overview of these func-tions by examining their graphs.A complete gallery of basicfunctions is included inAppendix B for easy reference.

Each basic function is revisitedlater in the book with a deeperanalysis that includes investiga-tion of the algebraic properties.

General characteristics of fami-lies of functions are also sum-marized.

Preface xv

Twelve Basic FunctionsThe Identity Function

f�x� � x

Interesting fact: This is the only function that acts on every realnumber by leaving it alone.

FIGURE 1.36

321

–1–2–3

y

x–5 –4 –3 –2 –1 321 4 5

The Squaring Function

f�x� � x2

Interesting fact: The graph of this function, called a parabola, hasa reflection property that is useful in making flashlights andsatellite dishes.

FIGURE 1.37

54321

–1

y

x–5 –4 –3 –2 –1 321 4 5

Exponential Functions f (x) � bx

Domain: All realsRange: �0, ��ContinuousNo symmetry: neither even nor oddBounded below, but not aboveNo local extremaHorizontal asymptote: y � 0No vertical asymptotes

If b � 1 (see Figure 3.3a), then

• f is an increasing function,• lim

x→��f �x� � 0 and lim

x→�f �x� � �.

If 0 � b � 1 (see Figure 3.3b), then

• f is a decreasing function,• lim

x→��f �x� � � and lim

x→�f �x� � 0.FIGURE 3.3 Graphs of f(x) � bx for (a) b � 1 and (b) 0 � b � 1.

y

x

f (x) = bx

b > 1

(0, 1)

(a)

(1, b)

y

x

f (x) = bx

0 < b < 1

(0, 1)

(b)

(1, b)

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xv

Applications and Real DataThe majority of the applications in the text are based on real data from cited sources, andtheir presentations are self-contained; students will not need any experience in the fieldsfrom which the applications are drawn.

As they work through the applications, students are exposed to func-tions as mechanisms for modeling data and are motivated to learnabout how various functions can help model real-life problems. Theylearn to analyze and model data, represent data graphically, interpretfrom graphs, and fit curves. Additionally, the tabular representation ofdata presented in this text highlights the concept that a function is acorrespondence between numerical variables. This helps studentsbuild the connection between the numbers and graphs and recognizethe importance of a full graphical, numerical, and algebraic under-standing of a problem. For a complete listing of applications, pleasesee the Applications Index on page 1015.

Content Changes to This EditionFor instructors, we have added additional coverage on topics that stu-dents usually find challenging, especially in Chapters 1, 2, and 9. Inaddition we have updated all the data in examples and exercises

wherever appropriate. We have also trimmed back cer-tain sections to better accommodate the length of theinstructional periods, and we’ve added extensiveresources for both new and experienced teachers. As aresult, we believe that the changes made in this editionmake this the most effective text available to students.

Chapter PComplex numbers are now introduced in Section P.6, which is earlier than their previousplacement in Chapter 2.

Chapter 1Section 1.4 from the previous edition has been split into two sections to give more prac-tice at function composition and to give inverse functions their own section. Graphical rep-resentations of absolute value compositions have been added.

Chapter 2The section on complex numbers has been moved to Chapter P to make the length of thischapter more teachable. Subsections titled “Applications of Quadratic Functions” and“Monomial Functions and Their Graphs” have been included to highlight these topics.

Chapter 4Exploration exercises have been added to introduce the arcsecant and arccosecant func-tions and the domain options associated with them.

Chapter 6The material of this chapter is now unified under the title “Applications of Trigonometry.”The section on vectors has been simplified, and there is a new subsection connecting thetopics of polar curves and parametric curves. Geometric representation of complex num-bers has been moved from Chapter 2 to Section 6.6.

Chapter 8The updated Chapter Project titled “Ellipses as Models of Pendulum Motion” addressesthe application of ellipses.

xvi Preface

Interpret

The model predicts the U.S. population was 301.3 million in 2003. The actual pop-ulation was 290.8 million. We overestimated by 10.5 million, less than a 4% error.

Now try Exercise 43.

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Chapter 9There are now separate sections for sequences and series, with more examples and exer-cises involving each, as well as expanded treatment of sequence convergence.

Chapter 10This preview of calculus first provides an historical perspective to calculus by presentingthe classical studies of motion through the tangent line and area problems. Limits are theninvestigated further, and the chapter concludes with graphical and numerical examinationsof derivatives and integrals.

New or Enhanced FeaturesSeveral features have been enhanced in this revision to assist students inachieving mastery of the skills and concepts of the course. We are pleased tooffer the following new or enhanced features.

Chapter Openers include a motivating photograph and a general descrip-tion of an application that can be solved with the topics in the chapter. Theapplication is revisited later in the chapter with a specific problem that issolved. These problems enable students to explore realistic situations usinggraphical, numerical, and algebraic methods. Students are also asked tomodel problem situations using the functions studied in the chapter. In addi-tion, the chapter sections are listed here.

A Chapter Overview begins each chapter to give you a sense of what youare going to learn. This overview provides a roadmap of the chapter, as wellas tells how the different topics in the chapter are connected under one bigidea. It is always helpful to remember that mathematics isn’t modular, butinterconnected, and that the skills and concepts you are learning throughoutthe course build on one another to help you understand more complicatedprocesses and relationships.

Similarly, the What you’lllearn about …and why fea-ture gives you the big ideas ineach section and explains theirpurpose. You should read this asyou begin the section andalways review it after you havecompleted the section to makesure you understand all of thekey topics that you have juststudied.

Preface xvii

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In Exercises 71 and 72, use the data in Table 3.28.

71. Modeling Population Find an exponential regression model forGeorgia’s population, and use it to predict the population in 2005.

72. Modeling Population Find a logistic regression model forIllinois’s population, and use it to predict the population in 2010.

Table 3.28 Populations of Two U.S.States (in millions)

Year Georgia Illinois

1900 2.2 4.81910 2.6 5.61920 2.9 6.51930 2.9 7.61940 3.1 7.91950 3.4 8.71960 3.9 10.11970 4.6 11.11980 5.5 11.41990 6.5 11.42000 8.2 12.4

Source: U.S. Census Bureau as reported in the WorldAlmanac and Book of Facts 2005.

Vocabulary is highlighted in yellow for easy reference. Properties are boxed ingreen so that you can easily find them.

Each example ends with a suggestion toNow Try a related exercise. Working thesuggested exercise is an easy way foryou to check your comprehension of thematerial while reading each section, insteadof waiting to the end of each section orchapter to see if you “got it.” In theAnnotated Teacher’s Edition, various exam-ples are marked for the instructor with the icon. Alternates are provided for theseexamples in the Acetates and Transparencies package.

Explorations appear throughout the text and provide you with the perfect opportunityto become an active learner and discover mathematics on your own. This will helphone your critical thinking and problem-solving skills. Some are technology-basedand others involve exploring mathematical ideas and connections.

Margin Notes on various topics appear throughout thetext. Tips offer practical advice to you on using yourgrapher to obtain the best, most accurate results.Margin notes include historical information, hintsabout examples, and provide additional insight to helpyou avoid common pitfalls and errors.

The Looking Ahead to Calculus icon is found throughout the text next to manyexamples and topics to point out conceptsthat students will encounter again in calcu-lus. Ideas that foreshadow calculus are high-lighted, such as limits, maximum and mini-mum, asymptotes, and continuity. Early in the text, the idea of the limit using an intu-itive and conceptual approach is introduced. Some calculus notation and language isintroduced in the early chapters and used throughout the text to establish familiarity.

The Web/Real Data icon is used to mark the examples and exercises that use realcited data.

The Chapter Review material at the end of each chapter are sec-tions dedicated to helping students review the chapter concepts. KeyIdeas has three parts: Properties, Theorems, and Formulas;Procedures; and Gallery of Functions. The Review Exercises repre-sent the full range of exercises covered in the chapter and give addi-tional practice with the ideas developed in the chapter. The exerciseswith red numbers indicate problems that would make up a goodpractice test. Chapter Projects conclude each chapter and requirestudents to analyze data. They can be assigned as either individual

Common Logarithms—Base 10Logarithms with base 10 are called . Because of their connec-tion to our base-ten number system, the metric system, and scientific notation, com-mon logarithms are especially useful. We often drop the subscript of 10 for the basewhen using common logarithms. The common logarithmic function log10 x � log xis the inverse of the exponential function f �x� � 10x. So

y � log x if and only if 10y � x.

Applying this relationship, we can obtain other relationships for logarithms withbase 10.

common logarithms

Basic Properties of Common Logarithms

Let x and y be real numbers with x � 0.

• log 1 � 0 because 100 � 1.

• log 10 � 1 because 101 � 10.

• log 10 y � y because 10 y � 10 y.

• 10log x � x because log x � log x.

xviii Preface

SOLUTION

(a) The graph of g�x� � e2x is obtained by horizontally shrinking the graph of f �x� �ex by a factor of 2 (Figure 3.7a).

(b) We can obtain the graph of h�x� � e�x by reflecting the graph of f �x� � ex acrossthe y-axis (Figure 3.7b).

(c) We can obtain the graph of k�x� � 3ex by vertically stretching the graph of f �x� �ex by a factor of 3 (Figure 3.7c). Now try Exercise 21.

EXAMPLE 5 Transforming Exponential FunctionsDescribe how to transform the graph of f �x� � ex into the graph of the given function.Sketch the graphs by hand and support your answer with a grapher.

(a) g�x� � e2x (b) h�x� � e�x (c) k�x� � 3ex

continued

A BIT OF HISTORY

Logarithmic functions were developedaround 1594 as computational tools byScottish mathematician John Napier(1550–1617). He originally called them“artificial numbers,” but changed thename to logarithms, which means“reckoning numbers.”

Graphs of Logarithmic Functions with Base bUsing the change-of-base formula we can rewrite any logarithmic function g�x� � logb x as

g�x� � �llnn

bx

� � �ln

1b

� ln x.

So every logarithmic function is a constant multiple of the natural logarithmic func-tion f �x� � ln x. If the base is b � 1, the graph of g�x� � logb x is a vertical stretch orshrink of the graph of f �x� � ln x by the factor 1�ln b. If 0 � b � 1, a reflection acrossthe x-axis is required as well.

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xviii

or group work. Each project expands upon concepts and ideastaught in the chapter, and many projects refer to the Web for furtherinvestigation of real data.

Exercise SetsEach exercise set begins with a Quick Review to help you reviewskills needed in the exercise set, thus reminding you again that math-ematics is not modular. There are also directions that give a section togo to for help so that students are prepared to do the SectionExercises.

There are over 6,000 exercises, including 680 Quick ReviewExercises. Following the Quick Review are exercises that allow youto practice the algebraic skills learned in that section. These exerciseshave been carefully graded from routine to challenging. The follow-ing types of skills are tested in each exercise set:

• Algebraic and analytic manipulation

• Connecting algebra to geometry

• Interpretation of graphs

• Graphical and numerical representations of functions

• Data analysis

Also included in the exercise sets are thought-provoking exercises:

• Standardized Test Questions include two true-false problemswith justifications and four multiple-choice questions.

• Explorations are opportunities for students to discover mathe-matics on their own or in groups. These exercises often requirethe use of critical thinking to explore the ideas.

Preface xix

CHAPTER 3 Project

Analyzing a Bouncing Ball

When a ball bounces up and down on a flat surface, the maxi-mum height of the ball decreases with each bounce. Eachrebound is a percentage of the previous height. For most balls,the percentage is a constant. In this project, you will use amotion detection device to collect height data for a ball bounc-ing underneath a motion detector, then find a mathematicalmodel that describes the maximum bounce height as a functionof bounce number.

Collecting the Data

Set up the Calculator Based Laboratory (CBL™) system witha motion detector or a Calculator Based Ranger (CBR™) sys-tem to collect ball bounce data using a ball bounce program forthe CBL or the Ball Bounce Application for the CBR. See theCBL/CBR guidebook for specific setup instruction.

Hold the ball at least 2 feet below the detector and release it sothat it bounces straight up and down beneath the detector.These programs convert distance versus time data to heightfrom the ground versus time. The graph shows a plot of sampledata collected with a racquetball and CBR. The data tablebelow shows each maximum height collected.

Bounce Number Maximum Height (feet)

0 2.71881 2.14262 1.65653 1.26404 0.983095 0.77783

Time (sec)

Hei

ght (

ft)

[0, 4.25] by [0, 3]

EXPLORATIONS

1. If you collected motion data using a CBL or CBR, a plot ofheight versus time should be shown on your graphing cal-culator or computer screen. Trace to the maximum heightfor each bounce and record your data in a table and useother lists in your calculator to enter this data. If you don’thave access to a CBL/CBR, enter the data given in the tableinto your graphing calculator/computer.

2. Bounce height 1 is what percentage of bounce height 0?Calculate the percentage return for each bounce. The num-bers should be fairly constant.

3. Create a scatter plot for maximum height versus bouncenumber.

4. For bounce 1, the height is predicted by multiplying bounceheight 0, or H, by the percentage P. The second height ispredicted by multiplying this height HP by P which givesthe HP2. Explain why y � HPx is the appropriate modelfor this data, where x is the bounce number.

5. Enter this equation into your calculator using your valuesfor H and P. How does the model fit your data?

6. Use the statistical features of the calculator to find the expo-nential regression for this data. Compare it to the equationthat you used as a model. y � 2.733 � 0.776x

7. How would your data and equation change if you used adifferent type of ball?

8. What factors would change the H value and what factorsaffect the P value?

9. Rewrite your equation using base e instead of using P as thebase for the exponential equation.

10. What do you predict the graph of ln (bounce height) versusbounce number to look like? Linear

11. Plot ln (bounce height) versus bounce number. Calculatethe linear regression and use the concept of logarithmic re-expression to explain how the slope and y-intercept arerelated to P and H.

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xix

• Writing to Learn exercises give you practice at communicating about mathematicsand opportunities to demonstrate your understanding of important ideas.

• Group Activity exercises ask you to work on the problems in groups or solve them asindividual or group projects.

• Extending the Ideas exercises go beyond what is presented in the textbook. Theseexercises are challenging extensions of the book’s material.

This variety of exercises provides sufficient flexibility to emphasize the skills most need-ed for each student or class.

Supplements and Resources

For the Student

Student Edition, ISBN 0-13-227650-X

Student’s Solutions Manual, ISBN 0-321-36994-7

• Contains detailed, worked-out solutions to odd-numbered exercises

Student Practice Workbook, ISBN 0-13-198580-9

• New examples that parallel key examples from each section in the book are provided,along with a detailed solution

• Related practice problems follow each example

Graphing Calculator Manual, ISBN 0-321-37000-7

• Grapher Workshop provides detailed instruction on important grapher features

• Features TI-83 Plus, Silver, TI-84, and TI-89 Titanium

For the Instructor

Annotated Teacher’s Edition, ISBN 0-321-37423-1

• Answers included on the same page for most exercises

• Notes on chapter and section objectives, suggested assignments, and teaching tipsappear in the margin

• Various examples are marked with the icon. Alternates are provided for theseexamples in the Acetates and Transparencies package.

• The Annotated Teacher’s Edition also includes notes written specifically for theteacher. These notes include chapter and section objectives, suggested assignments,lesson guides, and teaching tips.

Resource Manual, ISBN 0-321-36995-5

• Major Concepts Review, Group Activity Worksheets, Sample Chapter Tests,Standardized Test Preparation Questions, Contest Problems

Solutions Manual, ISBN 0-321-36993-9

• Complete solutions to all exercises, including Quick Reviews, Exercises,Explorations, and Chapter Reviews

Tests and Quizzes, ISBN 0-321-36992-0

• Two parallel tests per chapter, two quizzes for every 3–4 sections, two parallel mid-term tests covering Chapters P–5, two parallel end-of-year tests, covering Chapters6–10

xx Preface

OBJECTIVEStudents will be able to use exponentialgrowth, decay, and regression to modelreal-life problems.

MOTIVATE

Ask. . .If a culture of 100 bacteria is put into apetri dish and the culture doubles everyhour, how long will it take to reach400,000? Is there a limit to growth?

LESSON GUIDE

Day 1: Constant Percentage Rate andExponential Functions; ExponentialGrowth and Decay ModelsDay 2: Using Regression to ModelPopulation; Other Logisitic Models

FOLLOW-UP

Ask . . .If a � 0, how can you tell whether y �a • bx represents an increasing or decreasingfunction? (The function is increasing if b� 1 and decreasing if 0 � b � 1.)

ASSIGNMENT GUIDE

Day 1: Ex. 1–13 odd, 15–39, multiples of3, 45, 48Day 2: Ex. 41, 44, 49, 52, 53, 55, 65, 67,68, 70, 71

COOPERATIVE LEARNING

Group Activity: Ex. 39, 40

NOTES ON EXERCISES

Ex. 15–30 encourage students to thinkabout the appearance of functions withoutusing a grapher.Ex. 59–64 provide practice for standard-ized tests.Ex. 69–72 require students to think aboutthe meaning of different kinds of functions.

ONGOING ASSESSMENT

Self-Assessment: Ex. 1, 7, 11, 15, 21,41, 51, 55Embedded Assessment: Ex. 53, 68

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xx

Acetates and Transparencies, ISBN 0-321-36997-1

• Full color transparencies of 10–15 useful general transparencies along with black andwhite transparency masters of all Quick Review Exercises

• One Alternate Example per lesson

Technology ResourcesMathXL®, www.mathxl.com MathXL® is a powerful online homework, tutorial, and assessment system that accompaniesour textbooks in mathematics or statistics. With MathXL, instructors can create, edit, andassign online homework and tests using algorithmically generated exercises correlated at theobjective level to the textbook. They can also create and assign their own online exercisesand import TestGen tests for added flexibility. All student work is tracked in MathXL’sonline gradebook. Students can take chapter tests in MathXL and receive personalized studyplans based on their test results. The study plan diagnoses weaknesses and links studentsdirectly to tutorial exercises for the objectives they need to study and retest. Students canalso access video clips from selected exercises. For more information, visit our Web site atwww.mathxl.com, or contact your local sales representative.

MathXL® Tutorials on CD This interactive tutorial CD-ROM provides algorithmically generated practice exercisesthat are correlated at the objective level to the exercises in the textbook. Every practiceexercise is accompanied by an example and a guided solution designed to involve studentsin the solution process. Selected exercises may also include a video clip to help studentsvisualize concepts. The software provides helpful feedback for incorrect answers and cangenerate printed summaries of students’ progress.

InterAct Math Tutorial Web site, www.interactmath.comGet practice and tutorial help online! This interactive tutorial Web site provides algorith-mically generated practice exercises that correlate directly to the exercises in the textbook.Students can retry an exercise as many times as they like with new values each time forunlimited practice and mastery. Every exercise is accompanied by an interactive guidedsolution that provides helpful feedback for incorrect answers, and students can also viewa worked-out sample problem that steps them through an exercise similar to the one they’reworking on.

Video Lectures on CDThe video lectures for this text are also available on CD-ROM, making it easy and con-venient for students to watch the videos from a computer at home or on campus. The com-plete digitized video set, affordable and portable for students, is ideal for distance learningor supplemental instruction. These videotaped lectures feature an engaging team of math-ematics instructors who present comprehensive coverage of topics in the text.

TestGen®

TestGen® enables instructors to build, edit, print, and administer tests using a computer-ized bank of questions developed to cover all the objectives of the text. TestGen is algo-rithmically based, allowing instructors to create multiple but equivalent versions of thesame question or test with the click of a button. Instructors can also modify test bank ques-tions or add new questions. Tests can be printed or administered online. The software isavailable on a dual-platform Windows/Macintosh CD-ROM.

Preface xxi

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Presentation Express CD-ROM (PowerPoint® slides) This time saving component includes classroom presentation slides that correlate to thetopic sequence of the textbook. In addition, all transparencies are included in PowerPoint®format making it easier for you to teach and to customize based on your teaching prefer-ences. All slides can be customized and edited.

Teacher Express CD-ROM (with LessonView)

• This is a new suite of instructional tools on CD-ROM to help teachers plan, teach,and assess at the click of a mouse. Powerful lesson planning, resource management,testing, and an interactive Annotated Teacher’s Edition all in one place make classpreparation quick and easy!

• Contents include: Planning Express, Annotated Teacher’s Edition, Program TeachingResources, Correlations, Links to Other Resources.

• Online resources require an Internet Connection.

Student Express CD-ROM (with PDF Text) The perfect tool for test review or studying, this CD provides the complete student text-book in an electronic format.

Web SiteOur Web site, www.awl.com/demana, provides dynamic resources for instructors and stu-dents. Some of the resources include TI graphing calculator downloads, online quizzing,teaching tips, study tips, Explorations, and end-of-chapter projects.

xxii Preface

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xxii

xxiii

AcknowledgmentsWe wish to express our gratitude to the reviewers of this and previous editions who pro-vided such invaluable insight and comment. Special thanks is due to our consultant,Cynthia Schimek, Secondary Mathematics Curriculum Specialist, Katy Independent School District, Texas, for her guidance and invaluable insight on this revision.

Judy AckermanMontgomery College

Ignacio AlarconSanta Barbara City College

Ray BartonOlympus High School

Nicholas G. BelloitFlorida Community College at Jacksonville

Margaret A. BlumbergUniversity of Southwestern Louisiana

Ray CannonBaylor University

Marilyn P. CarlsonArizona State University

Edward ChampyNorthern Essex Community College

Janis M. CimpermanSaint Cloud State University

Wil ClarkeLa Sierra University

Marilyn CobbLake Travis High School

Donna CostelloPlano Senior High School

Gerry CoxLake Michigan College

Deborah A. CrockerAppalachian State University

Marian J. EllisonUniversity of Wisconsin—Stout

Donna H. FossUniversity of Central Arkansas

Betty GivanEastern Kentucky University

Brian GrayHoward Community College

Daniel HarnedMichigan State University

Vahack HaroutunianFresno City College

Celeste HernandezRichland College

Rich HoelterRaritan Valley Community College

Dwight H. HoranWentworth Institute of Technology

Margaret HovdeGrossmont College

Miles HubbardSaint Cloud State University

Sally JackmanRichland College

T. J. JohnsonHendrickson High School

Stephen C. KingUniversity of South Carolina—Aiken

Jeanne KirkWilliam Howard Taft High School

Georgianna KleinGrand Valley State University

Deborah L. Kruschwitz-ListUniversity of Wisconsin—Stout

Carlton A. LaneHillsborough Community College

James LarsonLake Michigan University

Edward D. LaughbaumColumbus State Community College

Ron MarshallWestern Carolina University

Janet MartinLubbock High School

5144_Demana_college_FMppi-xxiv 1/18/06 1:41 PM Page xxiii

Beverly K. MichaelUniversity of Pittsburgh

Paul MlakarSt. Mark’s School of Texas

John W. PetroWestern Michigan University

Cynthia M. PiezUniversity of Idaho

Debra PoeseMontgomery College

Jack PorterUniversity of Kansas

Antonio R. QuesadaThe University of Akron

Hilary RisserPlano West Senior High

Thomas H. RousseauSiena College

David K. RuchSam Houston State University

Sid SaksCuyahoga Community College

Mary Margaret Shoaf-GrubbsCollege of New Rochelle

Malcolm SouleCalifornia State University, Northridge

Sandy SpearsJefferson Community College

Shirley R. StavrosSaint Cloud State University

Stuart ThomasUniversity of Oregon

Janina UdrysSchoolcraft College

Mary VoxmanUniversity of Idaho

Eddie WarrenUniversity of Texas at Arlington

Steven J. WilsonJohnson County Community College

Gordon WoodwardUniversity of Nebraska

Cathleen Zucco-TeveloffTrinity College

xxiv Acknowledgments

We express special thanks to Chris Brueningsen, Linda Antinone, and Bill Bower for theirwork on the Chapter Projects. We would also like to thank Perian Herring, Frank Purcell,and Tom Wegleitner for their meticulous accuracy checking of the text. We are grateful toNesbitt Graphics, who pulled off an amazing job on composition and proofreading, andspecifically to Kathy Smith and Harry Druding for expertly managing the entire produc-tion process. Finally, our thanks as well are extended to the professional and remarkablestaff at Addison-Wesley, for their advice and support in revising this text, particularly AnneKelly, Becky Anderson, Greg Tobin, Rich Williams, Neil Heyden, Gary Schwartz, MarnieGreenhut, Joanne Ha, Karen Wernholm, Jeffrey Holcomb, Barbara Atkinson, EvelynBeaton, Beth Anderson, Maureen McLaughlin, and Michelle Murray. Particular recogni-tion is due Elka Block, who tirelessly helped us through the development and productionof this book.

—F. D. D.

—B. K. W.

—G. D. F.

—D. K.

Note to Instructors:The Annotated Teacher’s Edition contains answers to all exercises. Where space permits,answers appear on the same page as their corresponding exercises—either adjacent to theexercise or at the top or bottom of the exercise set—or answers appear in available spaceon the adjacent page. Where space does not permit answers to appear in the exercise set,those answers can be found in the back of the book.

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