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## Overview

Do your students attempt to memorize facts and mimic examples to make it through algebra? James Stewart, author of the worldwide, best-selling calculus texts, saw this scenario time and again in his classes. So, along with longtime coauthors Lothar Redlin and Saleem Watson, he wrote COLLEGE ALGEBRA specifically to help students learn to think mathematically and to develop genuine problem-solving skills. Comprehensive and evenly-paced, the text has helped hundreds of thousands of students. Incorporating technology, real-world applications, and additional useful pedagogy, the Seventh Edition promises to help more students than ever build conceptual understanding and a core of fundamental skills.

- Exercises - New Skills Plus exercises in most sections contain more challenging exercises that require students to extend and synthesize concepts. Additionally, more than 20% of the exercises are new, and groups of exercises now have headings that identify the type of exercise.
- Review Material - The review material at the end of each chapter now includes a Concept Check which provides a step-by-step review of all the main concepts and applications of the chapter. Answers to the Concept Check questions are in tear-out sheets at the back of the book.
- Discovery Projects - References to Discovery Projects, including brief descriptions of the content of each project, are located in boxes where appropriate in each chapter. These boxes highlight the applications of college algebra in many different real-world contexts. The projects are located at the book companion website www.stewartmath.com.
- Chapter P Prerequisites - This chapter now includes Section P.9 "Modeling with Equations." This section extends the theme of the introductory section P.1 "Modeling the Real World with Algebra" on the usefulness of algebra in solving real-world problems.
- Chapter 1 Coordinates and Graphs - This chapter has been reorganized. The chapter now begins with the coordinate plane and graphs of equations (including circles and lines), followed by sections on solving equations algebraically, and then a section on solving equations graphically. This last section shows the connections between graphs and the solutions of equations.
- Chapter 2 Functions - This chapter now includes the new Section 2.5, "Linear Functions and Models." This section highlights the connection between the slope of a line and the rate of change of a linear function. These two interpretations of slope help prepare students for the concept of the derivative in calculus.
- Chapter 3 Polynomial and Rational Functions - This chapter now includes the new Section 3.7, "Solving Polynomial and Rational Inequalities Graphically." Section 3.6, "Rational Functions," has a new subsection on rational functions with "holes." The sections on complex numbers and on variation have been moved to Chapter 1.
- Chapter 4 Exponential and Logarithmic Functions - The chapter now includes two sections on the applications of these functions. Section 4.7, "Modeling with Exponential Functions," focuses on modeling growth and decay, Newton's Law of Cooling, and other such applications. Section 4.8, "Logarithmic Scales," covers the concept of a logarithmic scale with applications involving the pH, Richter, and decibel scales.
- Chapter 5 Systems of Equations and Inequalities - The material on systems of inequalities has been rewritten to emphasize the steps used in graphing the solution of a system of inequalities.

- The new Get Ready feature at the beginning of a section lets students know which previous sections they need to have mastered before starting the section.
- Concept exercises, in addition to drill/skill exercises, vary from easy to difficult and help ensure that students are truly grasping the algebraic theories.
- Practice What You've Learned features at the end of each example directs students to a similar problem in the exercises, allowing them to immediately reinforce the concept just covered.
- Cumulative Reviews appear after select groups of chapters and help students gauge their progress and gain experience in taking tests that cover a broad range of concepts and skills.
- Enhanced WebAssign allows you to assign, collect, grade, and record homework assignments online, minimizing workload and streamlining the grading process. It also gives students the ability to stay organized with assignments and have up-to-date grade information.
- Many real-world applications show students how mathematics is used to model in fields such as engineering, physics, chemistry, business, and biology and help them relate the concepts they're studying to the world around them.
- Focus on Modeling sections show how algebra can be applied to model real-life situations.
- Optional, yet complete, technology applications for graphing calculators and computers appear throughout the text, giving you the flexibility to teach the course the way you want.

To the Student.

Prologue: Principles of Problem Solving.

P. PREREQUISITES.

P.1 Modeling the Real-World with Algebra. P.2 The Real Numbers. P.3 Integer Exponents and Scientific Notation. P.4 Rational Exponents and Radicals. P.5 Algebraic Expressions. P.6 Factoring. P.7 Rational Expressions. P.8 Solving Basic Equations. P.9 Modeling with Equations. Chapter P Review. Chapter P Test.

FOCUS ON MODELING: Making the Best Decisions.

1. EQUATIONS AND GRAPHS.

1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines.

1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test.

FOCUS ON MODELING: Fitting Lines to Data.

2. FUNCTIONS.

Chapter Overview.

2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models.

2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.

FOCUS ON MODELING: Modeling with Functions.

3. POLYNOMIAL AND RATIONAL FUNCTIONS.

Chapter Overview.

3.1 Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.

FOCUS ON MODELING: Fitting Polynomial Curves to Data.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Chapter Overview.

4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.

FOCUS ON MODELING: Fitting Exponential and Power Curves to Data.

5. SYSTEMS OF EQUATIONS AND INEQUALITIES.

5.1 Systems of Linear Equations in Two Variables. 5.2 Systems of Linear Equations in Several Variables. 5.3 Partial Fractions. 5.4 Systems of Nonlinear Equations. 5.5 Systems of Inequalities. Chapter 5 Review. Chapter 5 Test.

FOCUS ON MODELING: Linear Programming.

6. MATRICES AND DETERMINANTS.

6.1 Matrices and Systems of Linear Equations. 6.2 The Algebra of Matrices. 6.3 Inverses of Matrices and Matrix Equations. 6.4 Determinants and Cramer''s Rule. Chapter 6 Review. Chapter 6 Test.

FOCUS ON MODELING: Computer Graphics.

7. CONIC SECTIONS.

7.1 Parabolas. 7.2 Ellipses. 7.3 Hyperbolas. 7.4 Shifted Conics. Chapter 7 Review.

Chapter 7 Test.

FOCUS ON MODELING: Conics in Architecture.

8. SEQUENCES AND SERIES.

8.1 Sequences and Summation Notation. 8.2 Arithmetic Sequences. 8.3 Geometric Sequences. 8.4 Mathematics of Finance. 8.5 Mathematical Induction. 8.6 The Binomial Theorem. Chapter 8 Review. Chapter 8 Test.

FOCUS ON MODELING: Modeling with Recursive Sequences.

9. COUNTING AND PROBABILITY.

9.1 Counting. 9.2 Probability. 9.3 Binomial Probability. 9.4 Expected Value. Chapter 9 Review. Chapter 9 Test.

FOCUS ON MODELING: The Monte Carlo Method.

APPENDIX A: Calculations and Significant Figures.

APPENDIX B: Graphing with a Graphing Calculator.

APPENDIX C: Using the TI-83/84 Graphing Calculator.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

### FOR INSTRUCTORS

#### Electronic Test Bank

ISBN: 9781305257184

This supplement includes test forms for every chapter of the text, and can be found on the instructor companion site.

#### Cengage Learning Testing, powered by Cognero Instant Access

ISBN: 9781305255869

Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to author, edit, and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom or wherever you want. This is available online via www.cengage.com/login.

#### DVD

ISBN: 9781305257139

These text-specific DVDs cover all sections of the text—providing explanations of key concepts as well as examples, exercises, and applications in a lecture-based format.

#### Study Guide

ISBN: 9781305254800

This supplement provides students with additional exercises to guide them through the text and reinforce their understanding of key concepts.

#### Student Solutions Manual

ISBN: 9781305255890

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

### FOR STUDENTS

#### DVD

ISBN: 9781305257139

These text-specific DVDs cover all sections of the text—providing explanations of key concepts as well as examples, exercises, and applications in a lecture-based format.

#### Study Guide

ISBN: 9781305254800

This supplement provides students with additional exercises to guide them through the text and reinforce their understanding of key concepts.

#### Student Solutions Manual

ISBN: 9781305255890

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.