College Algebra: Graphs and Models, 7th edition
- Marvin L. Bittinger |
- Judith A. Beecher |
- Judith A. Penna |
- Barbara L. Johnson |
Title overview
For courses in College Algebra.
Students visualize, interact and succeed
College Algebra: Graphs and Models helps students “see the math” through its emphasis on visualization and technology, with a consistent focus on functions, side-by-side algebraic and graphical solutions, and real-data applications. Functions are presented as a thread that runs throughout the course rather than as an isolated topic. A variety of examples and exercises connect the mathematical content with everyday life, encouraging students to see and interpret the math that appears every day in their world.
The 7th Edition adds all-new Check Your Understanding exercises, adds a new Just-in-Time Review topic on Fractions and Mixed Numerals, expands introduction to nonlinear functions, and much more.
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.
- Real-data applications: A variety of examples and exercises connect the mathematical content with everyday life, encouraging students to see and interpret the math that appears every day in their world.
New and updated features of this title
- A new Just-in-Time Review topic on Fractions and Mixed Numerals (Topic 5) has been added to this revision.
- A set of 29 Just-in-Time prerequisite review topics, located before Chapter 1, supports concise review of individual topics as well as integrated review throughout the text. This feature provides a quick review of topics from intermediate algebra.
- New Check Your Understanding Exercises: These new brief sets of exercises appear immediately before each Exercise Set. Students can check and solidify their understanding of foundational concepts introduced in the section before beginning practice in the exercise set.
- Expanded Introduction to Nonlinear Functions: Chapter 2 now begins with an examination of different families of functions; students can explore types of functions through identification of graphs, applications, and piecewise functions.
- Later introduction to Zeros of Functions: Zeros are now introduced as part of the analysis of graphs of linear and nonlinear functions. This placement supports students' understanding of the concept with visualizations of functions with no zeros, one zero, and more than one zero.
Key features
Features of MyLab Math for the 7th Edition
- Updated Video Notebook: This author-created notebook contains fill-in-the-blank worksheets to accompany the authors’ video examples, along with key definitions, theorems and procedures. After filling in the worksheet while watching the video, the student has an excellent study guide for review and test preparation. (Available as a download in MyLab Math.)
- GeoGebra Exercises are gradable graphing exercises that help students demonstrate their understanding, enabling them to interact directly with the graph in a manner that reflects how they would graph on paper.
- Integrated Review Worksheets: 29 worksheets review prerequisite college algebra topics. An author-created correlation grid is available in the Instructor Resources section.
- Introduction to Key Topic Worksheets: 16 worksheets preview topics taught in college algebra. Some focus on an aspect of a topic that will foster a non-intimidating introduction; others suggest an intuitive approach to a concept. Many worksheets use visual elements like graphs to show students a big-picture perspective.
- Student Activities: A set of 21 activities guides students through collaborative, active learning as they explore a variety of concepts. There is at least 1 activity for each chapter.
- Mathematical Growth Mindset Activities: Written by author Barbara Johnson, these 7 activities help instructors approach selected course topics from different perspectives and discuss key aspects of growth mindset in the context of learning math.
Table of contents
- 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
- 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
Index of Applications
Author bios
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 Indianapolis. 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 Indianapolis. In addition to her career in textbook publishing she spends time traveling, enjoying her grandchildren, and promoting charity projects.
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 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.
Barbara Johnson is a Senior Lecturer in the Department of Mathematical Sciences at Indiana University Indianapolis, where she also serves as coordinator for the Mathematics for Elementary Teachers course sequence. She received her BS in mathematics from Bob Jones University, her MS in mathematics from Clemson University, and her PhD in Educational Studies from Ball State University. Dr. Johnson's areas of research are faculty professional development and affect in mathematics education. She also enjoys travel, hiking, gardening, and spending time with her family.