icon, to point out concepts that students will encounter again in calculus. Ideas that foreshadow calculus are highlighted, such as limits, maximum and minimum, asymptotes, and continuity.
Preface
Features
Changes to this Edition
Author bios
Frank Demana
Bert K. Waits
Gregory D. Foley
Daniel Kennedy
Supplements
Table of Contents
Our primary objectives are:
The Rule of Four - A Balanced Approach
A principal feature of this edition is the balance among the algebraic, numerical, graphical, and verbal methods of representing problems: the rule of four. For instance, we obtain solutions algebraically when that is the most appropriate technique to use, and we obtain solutions graphically or numerically when algebra is difficult to use. We urge students to solve problems by one method and then support or confirm their solutions by using another method. We believe that students must learn the value of each of these methods of representation and learn to choose the one most appropriate for solving the particular problem under 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 Approach
Systematic problem solving is emphasized in the examples throughout the text, using the following variation of Polya's problem-solving process:
Algebraic Skills and Understanding
Applications and Real Data
The majority of the applications described within the text are based on real data from cited sources, and their presentations are self-contained; students will not need any experience in the fields from which the applications are drawn. As they work through the applications, students are exposed to functions as mechanisms for modeling data and are motivated to learn about how various functions can help model real-life problems. They learn to analyze and model data, represent data graphically, interpret from graphs, and fit curves. Additionally, the tabular representation of data presented in this text highlights the concept that a function is a correspondence between numerical variables, helping students to build the connection between the numbers and graphs and recognize the importance of a full graphical, numerical, and algebraic understanding of the problem. For a complete listing of applications, please see the Index of Applications on page 1015.
Graphing Utilities
Students are expected to use a graphing utility (grapher) to visualize and solve problems. Throughout the text, the student is prompted to
Chapter Openers
Each chapter opens with a real life application. The answer to the application is given at the end of the section in which the appropriate concepts are covered. Frequently, real data is presented in these problems to enable students to explore realistic situations using graphical, numerical and algebraic methods. In other cases students are asked to model problem situations using the functions studied in the chapter.
Tips and Historical Notes
Tips throughout the text offer practical advice to students on using their grapher to obtain the best, most accurate results. Margin Notes include historical information, hints about examples, and provide additional insight to help students avoid common pitfalls and errors.
Exercise Sets
The exercise sets have been extensively revised for this edition. There are over 6000 exercises including 680 Quick Review Exercises that appear at the beginning of each exercise set. Following the Quick Review are exercises that allow students to practice the algebraic skills that they have learned in that section. These have been carefully graded from routine to challenging. The following types of exercises appear in each exercise set:
Also included in the exercise sets are thought-provoking exercises:
Math at Work
This feature introduces the student to individuals who are using mathematics in their jobs. Some of the applications of precalculus they encounter are mentioned throughout the text.
Chapter Review
At the end of each chapter are sections dedicated to helping the students review the chapter concepts and material. "Key Ideas" has four parts: Concepts; Properties, Theorems and Formulas; Procedures; and Gallery of Functions and each has appropriate page references. The "Review Exercises" contain the full range of exercises covered in the chapter. These exercises give students additional practice with the ideas developed in the chapter. The exercises with colored numbers indicate problems that we feel would make up a good practice test.
Chapter Projects
Each chapter concludes with a project that requires students to analyze data. These projects can be assigned as either individual or group work. Each project expands upon concepts and ideas taught in the chapter. Many projects refer students to the Web for further investigation of real data.
Looking Ahead to Calculus
One of the goals of this text is to help build an intuitive foundation for calculus.
icon, to point out concepts that students will encounter again in calculus. Ideas that foreshadow calculus are highlighted, such as limits, maximum and minimum, asymptotes, and continuity.
Changes to this edition
Chapter P: The new Prerequisites Chapter contains two new sections on solving equations and inequalities graphically and algebraically. The algebra review material has been moved to the new Appendix A. This new appendix will help students review, sharpen and hone their algebra skills.
Chapter 1: The basic functions are presented early in this chapter, enabling students to work with a richer variety of functions when learning the basic concepts – a benefit of grapher technology that fives coherence to the rest of the course. The idea of the limit is introduced conceptually along with limit notation to help describe end behavior and asymptotes. Graphical, algebraic, and numerical modeling with functions is emphasized from the beginning.
Chapter 2: This chapter covers polynomial, rational and power functions. The treatment of rational functions has been streamlined, but coverage of power functions has been extended. We introduce average rate of change of a function to show how the rate of change of a linear function can be related to slope. Students will encounter average rate of change again in calculus, and its inclusion in this chapter allows for the investigation of more interesting applications and models.
Chapter 3: The material in this chapter has been reorganized. We include more on mathematical modeling with special emphasis on this technique in Sections 3.2 and 3.5. We include more material on logistic functions and the natural base e, and also address the concept of "orders of magnitude."
Chapter 4: In this chapter we introduce the trigonometric functions using balanced algebraic and graphical approaches. This allows the students to better understand how the functions behave. We have moved the discussion of vectors to Chapter 6 to allow for a more extended treatment of this concept.
Chapter 5: This is the second of our new trigonometry chapters. Here, we use trigonometric identities to teach mathematical proof. We also use word ladders to illustrate the strategy for proving an identity. The inclusion of more "explorations" allows students to discover trigonometric relationships rather than just memorize them.
Chapter 6: This chapter is dedicated to the discussion of vectors and parametric and polar equations. Coverage of vectors has been extended to two sections, rather than one in this edition. The material on Parametric Equations has been consolidated into its own section, and is followed by sections on polar coordinates and polar equations.
Chapter 7: This chapter is a reorganization of Chapter 10 of the previous edition. We have included a new section on matrix algebra, and delayed our discussion of partial fractions until this chapter.
Chapter 8: The material in this chapter has also been reorganized. Coverage of conics has been expanded to three separate sections on parabolas, ellipses and hyperbolas for a more thorough and complete treatment. We have revised our approach to translations and rotations and have added a new section on three-dimensional analytic geometry. We feature a variety of applications of conics, including a great deal on reflective properties and applications to celestial mechanics.
Chapter 9: This is our chapter on Discrete Mathematics. The chapter is organized so that coverage of combinatorics appears before probability and the binomial theorem. The section on probability includes a discussion of conditional probability. Data analysis is emphasized throughout the chapter, especially in the statistics sections where we use real and up-to-date data in our examples and exercises.
Chapter 10: This introduction to calculus chapter is new to this text. The chapter first provides an historical perspective to calculus by presenting the classical studies of motion through the tangent line and area problems. Limits are then investigated further, and the chapter concludes with graphical and numerical examinations of derivatives and integrals.
Dr. Demana coauthored Essential Algebra: A Calculator Approach; Transition to College Mathematics; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; and Intermediate Algebra: A Graphing Approach; Calculus: Graphical, Numeric, Algebraic; Calculus: A Complete Course.
Bert K. Waits
Bert Waits received his Ph.D. from The Ohio State University and is currently Professor Emeritus there. Dr. Waits is cofounder of the national Teachers Teaching with Technology (T3) professional development program, and has been codirector or principal investigator on several large NSF projects. Dr. Waits has published articles in more that 50 nationally recognized professional journals. He frequently gives invited lectures, workshops, and minicourses at the national meetings of the MAA and the National Council of Teacher of Mathematics (NCTM) on how to use computer technology to enhance the teaching and learning of mathematics. He has given invited presentations at the International Congress on Mathematical Education (ICME 6, 7, and 8) in Budapest (1998), Quebec (1992), and Seville (1996). Dr. Waits is corecipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics, and is the cofounder (with Frank Demana) of the ICTCM. Dr. Waits was elected to be a member of the National Council of Teachers of Mathematics Board of Directors 2000-2002.
Dr. Waits coauthored Calculus: Graphical, Numerical, and Algebraic; Calculus: A Complete Course; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; and Intermediate Algebra: A Graphing Approach.
Gregory D. Foley
Gregory D. Foley is Distinguished Professor of Mathematics Education in the Department of Mathematical Sciences at Appalachian State University in Boone, North Carolina. He obtained B.A. and M.A. degrees in mathematics and a Ph.D. in mathematics education from The University of Texas at Austin. Dr. Foley has held faculty positions at North Harris County College, Austin Community College,, The Ohio State University, and Sam Houston State University. He is a member of the Academic Coordinator Council for the Teachers Teaching with Technology (T3) program, and the Committee on Research in Undergraduate Mathematics Education of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA). Dr. Foley has presented numerous talks internationally and has directed projects for high school mathematics teachers. In 1998, Dr. Foley received the biennial American Mathematical Association of Two-Year Colleges (AMATYC) Award for Mathematics Excellence for his lifetime achievements.
Daniel Kennedy
Dan Kennedy received his undergraduate degree from the College of the Holy Cross and his master's and Ph.D. in mathematics from the University of North Carolina at Chapel Hill. Since 1973 he has taught mathematics at the Baylor School in Chattanooga, Tennessee, where he holds the Cartter Lupton Distinguished professorship. Dr. Kennedy became an Advanced Placement Calculus reader in 1978, which led to an increasing level of involvement with the 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 require graphing calculators and laid the early groundwork for the recent reform of the Advanced Placement Calculus curriculum. The author of the 1997 Teacher's Guide—AP® Calculus, Dr. Kennedy has conducted more that 50 workshops and institutes for high school calculus teachers. His articles on mathematics teaching have appeared in the Mathematics Teacher and the American Mathematical Monthly, and he is a frequent speaker on calculus curriculum reform at professional 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 and Calculus: A Complete Course.
Graphing Calculator Manual (0-201-70068-9)
This manual contains keystroke level instructions for TI-82, TI-83, TI-83 plus, Casio CFX9850G Graphing Calculator, HP 38G and 48G, Sharp ELl-9200C and EL-9300C.
AWL Math Tutor Center:
Free tutoring is available to students who purchase a new copy of the fourth edition of Precalculus: Functions and Graphs. Qualified statistics and mathematics instructors providing students with tutoring on text examples, problems, and odd-numbered exercises staff the Addison Wesley Longman Math Tutor Center. Tutoring assistance is provided by telephone, fax, and e-mail and is available five days a week, seven hours a day. Each new book can be bundled with a registration number that provides each student with a free twelve-month subscription to the service. Request ISBN 0-201-71452-3 (text bundled with Tutor Center registration coupon). Students who already have their text may purchase a subscription to the Tutor Center by having their bookstore order ISBN 0-201-44461-5. For more information, please contact your Addison Wesley Longman sales consultant.
InterAct MathXL® (ISBN 0-201-71630-5)
Use our web-based diagnostic testing and tutorial system to improve your mathematics skills and understanding. You'll take a test on-line, receive a customized study plan based on your test results, be directed to practice problems in the topics you need to study, and receive help in areas you need to improve. After completing the study plan, you can then take the test again and see how much you've improved. InterAct MathXL uses the InterAct Math system for its tutorials and practice.
InterAct Math Tutorial CD-ROM (ISBN 0-201-69976-1)
This interactive tutorial software provides algorithmically generated practice exercises that correlate directly to the odd-numbered exercises in the text. A detailed worked-out example and guided solution accompany each practice exercise. The software recognizes common student errors and provides feedback.
| Chapter P: | Prerequisites | |
| P.1 | Real Numbers | |
| P.2 | Cartesian Coordinate System | |
| P.3 | Linear Equations and Inequalities | |
| P.4 | Solving Equations Graphically, Numerically, and Algebraically | |
| P.5 | Solving Inequalities Algebraically and Graphically | |
| Chapter 1: | Functions and Graphs | |
| 1.1 | Modeling and Equation Solving | |
| 1.2 | Functions and Their Properties | |
| 1.3 | Ten Basic Functions | |
| 1.4 | Building Functions from Functions | |
| 1.5 | Graphical Transformations | |
| 1.6 | Modeling with Functions | |
| Chapter 2: | Polynomial, Power and Rational Functions | |
| 2.1 | Linear and Quadratic Functions with Modeling | |
| 2.2 | Power Functions with Modeling | |
| 2.3 | Polynomial Functions of Higher Degree with Modeling | |
| 2.4 | Real Zeros of Polynomial Functions | |
| 2.5 | Complex Numbers | |
| 2.6 | Complex Zeros and the Fundamental Theorem of Algebra | |
| 2.7 | Rational Functions and Equations | |
| 2.8 | Solving Inequalities in One Variable | |
| Chapter 3: | Exponential, Logistic, and Logarithmic Functions | |
| 3.1 | Exponential and Logistic Functions | |
| 3.2 | Exponential and Logistic Modeling | |
| 3.3 | Logarithmic Functions and Their Graphs | |
| 3.4 | Properties of Logarithmic Functions | |
| 3.5 | Equation Solving and Modeling | |
| 3.6 | Mathematics of Finance | |
| Chapter 4: | Trigonometric Functions | |
| 4.1 | Angles and Their Measures | |
| 4.2 | Trigonometric Functions of Acute Angles | |
| 4.3 | Trigonometry Extended: The Circular Functions | |
| 4.4 | Graphs of Sine and Cosine: Sinusoids | |
| 4.5 | Graphs of Tangent, Cotangent, Secant, and Cosecant | |
| 4.6 | Graphs of Composite Trigonometric Functions | |
| 4.6 | Inverse Trigonometric Functions | |
| 4.6 | Solving Problems with Trigonometry | |
| Chapter 5: | Analytic Trigonometry | |
| 5.1 | Fundamental Identities | |
| 5.2 | Proving Trigonometric Identities | |
| 5.3 | Sum and Difference Identities | |
| 5.4 | Multiple-Angle Identities | |
| 5.5 | Law of Sines | |
| 5.6 | Law of Cosines | |
| Chapter 6: | Vectors and Parametric and Polar Equations | |
| 6.1 | Vectors in the Plane | |
| 6.2 | Dot Product of Vectors | |
| 6.3 | Parametric Equations and Motion | |
| 6.4 | Polar Coordinates | |
| 6.5 | Graphs of Polar Equations | |
| 6.6 | De Moivre's Theorem and nth Roots | |
| Chapter 7: | Systems and Matrices | |
| 7.1 | Solving Systems of Two Equations | |
| 7.2 | Matrix Algebra | |
| 7.3 | Multivariate Linear Systems and Row Operations | |
| 7.4 | Partial Fractions | |
| 7.5 | Systems of Inequalities in Two Variables | |
| Chapter 8: | Analytic Geometry in Two and Three Dimensions | |
| 8.1 | Conic Sections and Parabolas | |
| 8.2 | Ellipses | |
| 8.3 | Hyperbolas | |
| 8.4 | Translations and Rotations of Axes | |
| 8.5 | Polar Equations of Conics | |
| 8.6 | Three Dimensional Cartesian Coordinate System | |
| Chapter 9: | Discrete Mathematics | |
| 9.1 | Basic Combinatorics | |
| 9.2 | The Binomial Theorem | |
| 9.3 | Probability | |
| 9.4 | Sequences and Series | |
| 9.5 | Mathematical Induction | |
| 9.6 | Statistics and Data (Graphical) | |
| 9.6 | Statistics and Data (Algebraic) | |
| Chapter 10: | An Introduction to Calculus: Limits, Derivatives, and Integrals | |
| 10.1 | Limits and Motion: The Tangent Problem | |
| 10.2 | Limits and Motion: The Area Problem | |
| 10.3 | More on Limits | |
| 10.4 | Numerical Derivatives and Integrals | |
|
© 2000 by Addison Wesley Longman A division of Pearson Education |