Precalculus (6^th Ed.)
Graphs and Models, A Right Triangle Approach

For courses in precalculus.

Visualize. Interact. Succeed.

The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students “see the math” through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications. With the Sixth Edition, visualization is taken to a new level with technology, and students find even more ongoing review.

Also available with MyMathLab

MyMathLab^® is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

New Guided Visualizations in MyMathLab help students allow for hands-on manipulation to gain understanding of difficult concepts. References to 28 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most, and new Cumulative Review Assignments and Skill Maintenance Quizzes are pre-made and assignable in MyMathLab to help students connect concepts and maintain skills throughout the course.  Plus, new Video Assessment Exercises and a new Video Notebook further enhance the MyMathLab course and resources available.

Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyMathLab, search for:

0134379950 / 9780134379951 * Precalculus: Graphs and Models plus MyMathLab with Pearson eText -- Access Card Package

Package consists of:

0134179056 / 9780134179056 * Precalculus: Graphs and Models

0321431308 / 9780321431301 * MyMathLab -- Glue-in Access Card

Preface

To the Student

Just-In-Time Review

1. Graphs, Functions, and Models

1.1 Introduction to Graphing

   Visualizing the Graph

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

   Visualizing the Graph

   Mid-Chapter Mixed Review

1.4 Equations of Lines and Modeling

1.5 Linear Equations, Functions, Zeros, and Applications

1.6 Solving Linear Inequalities

   Study Guide

   Review Exercises

   Test

2. More on Functions

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

   Mid-Chapter Mixed Review

2.4 Symmetry

2.5 Transformations

   Visualizing the Graph

2.6 Variation and Application

   Study Guide

   Review Exercises

   Test

3. Quadratic Functions and Equations; Inequalities

3.1 The Complex Numbers

3.2 Quadratic Equations, Functions, Zeros, and Models

3.3 Analyzing Graphs of Quadratic Functions

   Visualizing the Graph

   Mid-Chapter Review

3.4 Solving Rational Equations and Radical Equations

3.5 Solving Equations and Inequalities with Absolute Value

   Study Guide

   Review Exercises

   Test

4. Polynomial Functions and Rational Functions

4.1 Polynomial Functions and Modeling

4.2 Graphing Polynomial Functions

   Visualizing the Graph

4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

   Mid-Chapter Mixed Review

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

   Visualizing the Graph

4.6 Polynomial Inequalities and Rational Inequalities

   Study Guide

   Review Exercises

   Test

5. Exponential Functions and Logarithmic Functions

5.1 Inverse Functions

5.2 Exponential Functions and Graphs

5.3 Logarithmic Functions and Graphs

   Visualizing the Graph

   Mid-Chapter Mixed Review

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential Equations and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; Compound Interest

   Study Guide

   Review Exercises

   Test

6. The Trigonometric Functions

6.1 Trigonometric Functions of Acute Angles

6.2 Applications of Right Triangles

6.3 Trigonometric Functions of Any Angle

   Mid-Chapter Mixed Review

6.4 Radians, Arc Length, and Angular Speed

6.5 Circular Functions: Graphs and Properties

6.6 Graphs of Transformed Sine Functions and Cosine Functions

   Visualizing the Graph

   Study Guide

   Review Exercises

   Test

7. Trigonometric Identities, Inverse Functions, and Equations

7.1 Identities: Pythagorean and Sum and Difference

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

7.3 Proving Trigonometric Identities

   Mid-Chapter Mixed Review

7.4 Inverses of the Trigonometric Functions

7.5 Solving Trigonometric Equations

   Visualizing the Graph

   Study Guide

   Review Exercises

   Test

8. Applications of Trigonometry

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Complex Numbers: Trigonometric Notation

   Mid-Chapter Mixed Review

8.4 Polar Coordinates and Graphs

   Visualizing the Graph

8.5 Vectors and Applications

8.6 Vector Operations

   Study Guide

   Review Exercises

   Test

9. Systems of Equations and Matrices

9.1 Systems of Equations in Two Variables

   Visualizing the Graph

9.2 Systems of Equations in Three Variables

9.3 Matrices and Systems of Equations

9.4 Matrix Operations

   Mid-Chapter Mixed Review

9.5 Inverses of Matrices

9.6 Determinants and Cramer’s Rule

9.7 Systems of Inequalities and Linear Programming

6.8 Partial Fractions

   Study Guide

   Review Exercises

   Test

10. Analytic Geometry Topics

10.1 The Parabola

10.2 The Circle and the Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Inequalities

   Visualizing the Graph

   Mid-Chapter Mixed Review

10.5 Rotation of Axes

10.6 Polar Equations of Conics

10.7 Parametric Equations

   Study Guide

   Review Exercises

   Test

11. Sequences, Series, and Combinatorics

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

   Visualizing the Graph

11.4 Mathematical Induction

   Mid-Chapter Mixed Review

11.5 Combinatorics: Permutations

11.6 Combinatorics: Combinations

11.7 The Binomial Theorem

11.8 Probability

   Study Guide

   Review Exercises

   Test

Photo Credits

Answers // Additional Instructor’s Answers

Index

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University—Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife, Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp.

David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's

• Functions appear early and are integrated throughout the text, reflecting the authors' belief that functions are best taught as a theme of the course—not as an isolated topic.
  • Functions are introduced in Chapter 1, so that students start the course with a new topic rather than a review of equation-solving that was covered in previous math courses.
  • Students come to understand the concept of a function by being exposed repeatedly to the language, notation, and use of functions throughout the text.
  • Graphs are used frequently to provide a visual component to solving equations and inequalities.
• The visual approach of the authors enables students to “see the math” and quickly make connections between concepts.
  • Visualizing the Graph exercises help develop students’ ability to make the mental link between different types of equations and their corresponding graphs. In addition to the full-page feature within the chapters, a unique exercise-type asks students to match equations with their graphs.
  • Algebraic/Graphical Side-by-Side Examples present the solutions in a two-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.
  • Guided Visualizations are available in MyMathLab, enabling users to manipulate figures to bring hard-to-convey math concepts to life. These are also assignable, giving instructors one more tool to promote understanding.
  • Annotated Examples show step-by-step procedures, and employ color-coded art to guide students through the process of learning and understanding the concepts.
  • Now Try questions, following every example, encourage active learning by asking students to do an exercise in the exercise set that is similar to the example.
• Ongoing review feat