College Algebra: Graphs and Models, 3rd Edition

ISBN10: 0077221281 | ISBN13: 9780077221287

By Raymond Barnett, Michael Ziegler, Karl Byleen and David Sobecki

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ISBN10: 0077221281 | ISBN13: 9780077221287

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Complete text bound in hardcover or softcover

* The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

Instructor Details

Overview

The Barnett Graphs & Models series in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and processes.

A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.

Table of Contents

CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS

1-1 Using Graphing Utilities

1-2 Functions

1-3 Functions: Graphs and Properties

1-4 Functions: Graphs and Transformations

1-5 Operations on Functions; Composition

1-6 Inverse Functions

Chapter 1 Review

Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long Distance Calling Plan

CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNCTIONS

2-1 Linear Functions

2-2 Linear Equations and Models

2-3 Quadratic Functions

2-4 Complex Numbers

2-5 Quadratic Equations and Models

2-6 Additional Equation Solving Techniques

2-7 Solving Inequalities

Chapter 2 Review

Chapter 2 Group Activity: Mathematical Modeling in Population Studies

Cumulative Review Exercise for Chapters 1 and 2

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS

3-1 Polynomial Functions And Models

3-2 Polynomial Division

3-3 Real Zeros and Polynomial Inequalities

3-4 Complex Zeros and Rational Zeros of Polynomials

3-5 Rational Functions and Inequalities

3-6 Variation and Modeling

Chapter 3 Review

Chapter 3 Group Activity: Interpolating Polynomials

CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS

4-1 Exponential Functions

4-2 Exponential Models

4-3 Logarithmic Functions

4-4 Logarithmic Models

4-5 Exponential and Logarithmic Equations

Chapter 4 Review

Chapter 4 Group Activity: Comparing Regression Models

Cumulative Review Exercise for Chapters 3 and 4

CHAPTER 5 MODELING WITH SYSTEMS OF EQUATIONS AND INEQUALITIES

5-1 Systems of Linear Equations in Two Variables

5-2 Systems of Linear Equations in Three Variables

5-3 Systems of Linear Inequalities

5-4 Linear Programming

Chapter 5 Review

Chapter 5 Group Activity: Modeling with Systems of Equations

CHAPTER 6 MATRICES AND DETERMINANTS

6-1 Matrix Solutions to Linear Systems

6-2 Matrix Operations

6-3 Inverse of a Square Matrix

6-4 Matrix Equations and Systems of Linear Equations

6-5 Determinants

6-6 Properties of Determinants

6-7 Determinants and Cramer's Rule

Chapter 6 Review

Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue, and Profit

Cumulative Review Exercise for Chapters 5 and 6

CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY

7-1 Sequences and Series

7-2 Mathematical Induction

7-3 Arithmetic and Geometric Sequences

7-4 Multiplication Principle, Permutations, and Combinations

7-5 Sample Spaces and Probability

7-6 Binomial Formula

Chapter 7 Review

Chapter 7 Group Activity: Sequences Specified by Recursion Formulas

8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

8-1 Conic Sections; Parabola

8-2 Ellipse

8-3 Hyperbola

8-4 Systems of Nonlinear Equations

Chapter 8 Review

Chapter 8 Group Activity: Focal Chords

Cumulative Review Exercise for Chapters 7 and 8

Appendix A BASIC ALGEBRA REVIEW

A-1 Algebra and Real Numbers

A-2 Exponents

A-3 Radicals

A-4 Polynomials: Basic Operations

A-5 Polynomials: Factoring

A-6 Rational Expressions: Basic Operations

Appendix A Review

Appendix A Group Activity: Rational Number Representations

Appendix B REVIEW OF EQUATIONS AND GRAPHING

B-1 Linear Equations and Inequalities

B-2 Cartesian Coordinate System

B-3 Basic Formulas in Analytic Geometry

Appendix C SPECIAL TOPICS

C-1 Significant Digits

C-2 Partial Fractions

C-3 Descartes' Rule of Signs

C-4 Parametric Equations

Appendix D GEOMETRIC FORMULAS

Author Bios

About the Author

Raymond Barnett

Michael Ziegler

Karl Byleen

David Sobecki

I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. I’ve won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. I’ve written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS. After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetson’s-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. “Because we’ve always done it that way” is NOT a good reason to maintain the status quo in our curriculum. Let’s work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think I’m in the right place at the right time to make a difference in the new and exciting pathways course. I’m in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Don’t tell my publisher this – they think I spend 20 hours a day working on textbooks – but I’m working on my first novel in the limited spare time that I have.) I’m also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement.

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