College Algebra: Graphs and Models

For courses in college algebra.

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:

0134265211 / 9780134265216 * College Algebra: Graphs and Models Plus MyMathLab with Pearson eText -- Access Card Package

Package consists of:

013417903X / 9780134179032 * College Algebra: Graphs and Models

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

0321654064 / 9780321654069 * MyMathLab Inside Star Sticker

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 College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.

Preface

To the Student

Just-in-Time Review

            1. Real Numbers

            2. Properties of Real Numbers

            3. Order on the Number Line

            4. Absolute Value

            5. Operations with Real Numbers

            6. Interval Notation

            7. Integers as Exponents

            8. Scientific Notation

            9. Order of Operations

            10. Introduction to Polynomials

            11. Add and Subtract Polynomials

            12. Multiply Polynomials

            13. Special Products of Binomials

            14. Factor Polynomials; The FOIL Method

            15. Factor Polynomials: The ac-Method

            16. Special Factorizations

            17. Equation-Solving Principles

            18.  Inequality-Solving Principles

            19. The Principle of Zero Products

            20. The Principle of Square Roots

            21. Simplify Rational Expressions

            22. Multiply and Divide Rational Expressions

            23. Add and Subtract Rational Expressions

            24. Simplify Complex Rational Expressions

            25. Simplify Radical Expressions

            26. Rationalize Denominators

            27. Rational Exponents

            28. The Pythagorean Theorem

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

            Summary and Review

            Review Exercises

            Chapter 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 Applications

            Summary and Review

            Review Exercises

            Chapter 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 Mixed Review

3.4. Solving Rational Equations and Radical Equations

3.5. Solving Equations and Inequalities with Absolute Value

            Summary and Review

            Review Exercises

            Chapter 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

            Chapter 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   364

            Study Guide

            Review Exercises

            Chapter Test

6. Systems of Equations and Matrices

6.1. Systems of Equations in Two Variables

            Visualizing the Graph

6.2. Systems of Equations in Three Variables

6.3. Matrices and Systems of Equations

6.4. Matrix Operations

            Mid-Chapter Mixed Review

6.5. Inverses of Matrices

6.6. Determinants and Cramer’s Rule

6.7. Systems of Inequalities and Linear Programming

6.8. Partial Fractions

            Study Guide

            Review Exercises

            Chapter Test

7. Conic Sections

7.1. The Parabola

7.2. The Circle and the Ellipse

            Mid-Chapter Mixed Review

7.3. The Hyperbola

7.4. Nonlinear Systems of Equations and Inequalities

            Visualizing the Graph

            Study Guide

            Review Exercises

            Chapter Test

8. Sequences, Series, and Combinatorics

8.1. Sequences and Series

8.2. Arithmetic Sequences and Series

8.3. Geometric Sequences and Series

            Visualizing the Graph

8.4. Mathematical Induction

            Mid-Chapter Mixed Review

8.5. Combinatorics: Permutations

8.6. Combinatorics: Combinations

8.7. The Binomial Theorem

8.8. Probability

            Study Guide

            Review Exercises

            Chapter Test

Photo Credits

Answers

Additional Instructor’s Answers

Index

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.