# Algebra and Trigonometry: Graphs and Models, 6th edition

Published by Pearson (January 14, 2016) © 2017

**Marvin L. Bittinger**Indiana University Purdue University Indianapolis**Judith A. Beecher**Indiana University Purdue University Indianapolis**David J. Ellenbogen**Community College of Vermont**Judith A. Penna**Indiana University Purdue University Indianapolis

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## MyLab

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For courses in Algebra & Trigonometry.

### Visualize. Interact. Succeed.

**Algebra and Trigonometry: Graphs and Models** helps students “see the math” through its focus on visualization and technology. Its consistent approach of focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications helps students succeed. The **6th Edition** enhances instruction on review topics both for today's corequisite courses and for students who come to the course underprepared. Integrated review gives students just the help they need when they need it.

### Hallmark features of this title

**Functions**appear early and are integrated throughout.**Graphs**are used frequently in solving equations and inequalities.**Visualizing the Graph exercises**develop students' ability to connect different types of equations and their corresponding graphs.**Algebraic/Graphical Side-by-Side Examples**present solutions in a 2-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.**Annotated Examples**show step-by-step procedures and use color-coded art to guide students.**Now Try questions**follow every example, asking students to do an exercise in the exercise set that is similar to the example.**Ongoing review features**throughout reinforce concepts and help students build understanding.

### New and updated features of this title

**Ongoing Review**is placed as needed throughout the text.**Just-In-Time Review**of prerequisite algebra topics is now referenced when students need it most.**28 Just-In-Time review topics**are referenced throughout the text and MyLab Math course to create an efficient review of intermediate algebra topics.**Just-In-Time icons**appear next to examples where review of an intermediate algebra topic would be helpful, directing students to the review topics in the front of the text.

**Chapter R**has been moved to MyLab Math.

### Highlights of the DIGITAL UPDATE for MyLab Math

Instructors, contact your sales rep to ensure you have the most recent version of the course.

The **Digital Update **to **Algebra and Trigonometry: Graphs and Models, 6/e ** now offers Integrated Review to help underprepared students plus an expanded, robust video program.

### Features of MyLab Math for the 6th Edition

**Integrated Review**gives targeted remediation with Skills Check Quizzes, Personalized Skills Review Homework, Exercises, new Videos, and the new Corequisite Notebook Worksheets. The new Corequisite Resource Notebook corresponds with the integrated review content.**Updated Just-in-Time videos**review the prerequisite topic needed for the chapter and the Corequisite Resource Notebook worksheets.**New Example videos**have retained the same examples but now highlight the GeoGebra graphing utility, reflecting graphing technology expands beyond graphing calculators.**New Preview Videos**walk students through introductory examples of what is coming up in the chapter.**New Personal Assessment Inventories**is a collection of online activities designed to promote self-reflection and engagement in students.**New Mindset videos**and assignable, open-ended**exercises**foster a growth mindset in students.

- 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
- 9.8 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

#### Index of Applications

### About our authors

**Marvin Bittinger **has taught math at the university level for more than 38 years, and he is now Professor Emeritus of mathematics education at Indiana University - Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra & 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. 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, particularly apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 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 nearly 30 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 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 (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master's degree in community college mathematics education from The University of Massachusetts - Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has 2 sons, Monroe and Zachary.

**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.

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