College Algebra Enhanced with Graphing Utilities / Edition 7

by Michael Sullivan

Overview

NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value—this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products.

Prepare, Practice, Review

The Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Series has evolved to meet today’s course needs by integrating the usage of graphing calculators, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.

In the Seventh Edition, there are several new features that appear in both the text and MyMathLab. Retain Your Knowledge problems offer the type of “final exam material” that students can use to maintain their skills throughout each chapter.

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 Lecture Notes help students take thorough, organized, and understandable notes during class or while they watch the Author in Action videos. They ask students to complete definitions, procedures, and examples based on the content of the videos and text.

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.

Product Details

ISBN-13:	9780134111353
Publisher:	Pearson Education
Publication date:	01/08/2016
Edition description:	7th ed.
Pages:	864
Product dimensions:	8.40(w) x 10.80(h) x 1.00(d)

About the Author

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between Oak Lawn, Illinois, and Naples, Florida.

Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows, and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.

Mike has been writing textbooks for more than 35 years and currently has 15 books in print, 12 with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.

Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on two precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.

Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer, who tries to spend as much of his limited free time as possible on the golf course.

Table of Contents

(NOTE: Each chapter concludes with Chapter Review.)
R. Review.
Real Numbers. Algebra Review. Geometry Review. Integer Exponents.Polynomials. Factoring Polynomials. Rational Expressions. Square Roots;Radicals. Rational Exponents.

1. Graphs.
Rectangular Coordinates; Graphing Utilities. Introductionto Graphing Equations. Solving Equations Using a Graphing Utility;Linear and Quadratic Equations. Setting up Equations; Applications.Radical Equations; Equations Quadratic in Form; Absolute Value Equations.Solving Inequalities. Lines. Circles. Chapter Projects.

2. Linear and Quadratic Functions.
Functions. Linear Functions and Models. Quadratic Functions.Quadratic Models. Chapter Projects. Cumulative Review.

3. Functions and Their Graphs.
Symmetry; Graphing Key Equations. Properties of Functions.Library of Functions; Piecewise-Defined Functions. Graphing Techniques:Transformations. Operations on Functions; Composite Functions. MathematicalModels: Constructing Functions. Chapter Projects. Cumulative Review.

4. Polynomial and Rational Functions.
Power Functions and Models. Polynomial Functions and Models.Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomialand Rational Inequalities. Chapter Projects. Cumulative Review.

5. The Zeros of a Polynomial Function.
Synthetic Division. The Real Zeros of a Polynomial Function.Complex Numbers; Quadratic Equations with a Negative Discriminant.Complex Zeros; Fundamental Theorem of Algebra. Chapter Projects. CumulativeReview.

6. Exponential and Logarithmic Functions.
One-to-One Functions; Inverse Functions.Exponential Functions.Logarithmic Functions. Properties of Logarithms. Logarithmic and ExponentialEquations. Compound Interest. Growth and Decay. Exponential, Logarithmic,and Logistic Curve Fitting. Chapter Projects. Cumulative Review.

7. Systems of Equations and Inequalities.
Systems of Linear Equations: Two Equations Containing TwoVariables. Systems of Linear Equations: Three Equations ContainingThree Variables. Systems of Linear Equations: Matrices. Systems ofLinear Equations: Determinants. Matrix Algebra. Systems of LinearInequalities; Linear Programming. Partial Fraction Decomposition.Chapter Projects. Cumulative Review.

8. Sequences; Induction; the Binomial Theorem.
Sequences. Arithmetic Sequences. Geometric Sequences; GeometricSeries. Mathematical Induction. The Binomial Theorem. Chapter Projects.Cumulative Review.

9. Counting and Probability.
Sets and Counting. Permutations and Combinations. Probabilityof Equally Likely Outcomes. Obtaining Probabilities from Data. ChapterProjects. Cumulative Review.

10. Conics.
Preliminaries. The Parabola. The Ellipse. The Hyperbola.Systems of Nonlinear Equations. Chapter Projects. Cumulative Review.

Answers.
Index.

Introduction

As professors at both an urban public university and a community college, Michael Sullivan and Michael Sullivan, III are aware of the varied needs of College Algebra students, ranging from those who have little mathematical background and a fear of mathematics courses, to those having a strong mathematical education and a high level of motivation. For some of your students, this will be their last course in mathematics, while others will further their mathematical education. This text is written for both groups.

As a teacher, and as an author of precalculus, engineering calculus, finite math, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level math courses. However, as a father of four, including the coauthor, he also understands the realities of college life. His co-author and son, Michael Sullivan III, believes passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills. Together, both authors have taken great pains to ensure that the text contains solid, student-friendly examples and problems, as well as a clear and seamless writing style. We encourage you to share with us your experiences teaching from this text.

In the Third Edition

The third edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. One important benefit of authoring a successful series is the broad-based feedback upon whichimprovements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made by colleagues and students who have used previous editions. This feedback has proved invaluable and has been used to make changes that improve the flow, usability, and accessibility of the text. For example, some topics have been moved to better reflect the way teachers approach the course and problems have been added where more practice was needed. The supplements package has been enhanced through upgrading traditional supplements and adding innovative media components.

Reorganized Content for College Algebra

• Appendix Review
• Now expanded, this material appears in the beginning of the book as Chapter R
• Chapter 1
• Scatter diagrams now appear in Section 2.2 Linear Functions and Models
• Section 1.2 has been split into two sections. In 3/e Section 1.2 contains point plotting, graphing equations on a graphing utility, and intercepts. Section 3.1 covers symmetry and graphing key equations. This adheres to the "just in time approach" by placing symmetry and key equations closer to functions.
• Section 1.3 from 2/e has been split into two sections—1.3 and 1.5. Section 1.5 has been expanded to include quadratic-in-form equations.
• Chapter 2
• Section 2.2 now includes the discussion on scatter diagrams.
• Quadratic equations now appears earlier as part of Section 1.3.
• Chapter 3
• Section 3.1 contains the discussion on symmetry and graphing key equations.
• Section 3.1 from 2/e is now two sections: Section 3.2 covers properties of functions, while Section 3.3 covers the library of functions and piecewise-defined functions.
• Chapter 4
• This chapter contains Sections 4.1, 4.2, 4.7 and 4.8 from 2/e. The section on rational functions has been split into two sections to accommodate a single lecture for each section.
• Chapter 5
• This chapter contains the remaining sections of Chapter 4 from 2/e.
• Chapter 6 (Formerly Chapter 5)
• Section 6.2 now includes a discussion of basic exponential equations.
• Section 6.3 now includes a discussion of basic logarithmic equations.
• Chapter 7 (Formerly Chapter 6)
• Chapter 8 (Formerly Chapter 7)
• Chapter 9 (Formerly Chapter 8)
• Chapter 10 (Formerly Chapter 9)

Specific Content Changes

In this edition emphasis is placed on the role of modeling in college algebra. To this end, dedicated sections appear on Linear Functions and Models, Quadratic Models, Power Functions and Models, Polynomial Functions and Models, Exponential and Logarithmic Functions and Models. Many of these applications focus on the areas of business, finance, and economics.

Chapter R is a robust expansion of the Appendix Review of the second edition.

New to this edition is a discussion of quadratic-in-form equations.

As a result of these changes, this edition will be an improved teaching device for professors and a better learning tool for students.

Features in the 3^rd Edition

• Section OBJECTIVES appear in a numbered list to begin each section.
• "Now Work" problems identified by the yellow pencil icon appear after a concept has been introduced. This directs the student to a problem in the exercises that tests the concept, insuring that the concept has been mastered before moving on.
• References to calculus are identified by a calculus icon.
• Historical Perspectives, sometimes with exercises, are presented in context and provide interesting anecdotal information.
• Varied applications and real-world data are abundant in Examples and in Exercises. Many contain sourced data.
• Discussion, Writing, and Research problems appear in most exercise sets, identified by an icon and red numbers. These problems challenge students to expand the parameters of their understanding by providing the basis for class discussions, writing projects and collaboration.
• An extensive Chapter Review provides a list of important formulas, definitions, theorems, and objectives. Each objective is listed with a page reference and review exercises that test the student's understanding of the objective. The authors' suggestions for practice tests are indicated in blue.
• A Cumulative Review appears at the end of every chapter, beginning with Chapter 2. These cumulative reviews serve to continually reinforce skills from previous chapters. This makes study for the final examination easier.

Using the 3^rd Edition Effectively and Efficiently with Your Syllabus

To meet the varied needs of diverse syllabi, this book contains more content than a typical college algebra course. The illustration shows the dependencies of chapters on each other. As the chart indicates, this book has been organized with flexibility of use in mind. Even within a given chapter, certain sections can be skipped without fear of future problems.

Chapter R Review

This chapter is a revision of the Appendix in the second edition. It may be used as the first part of the course, or as a "just-in-time" review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.

Chapter 1: Graphs

This chapter presents an introduction to graphing and the graphing utility. Equations and inequalities are solved algebraically with graphical support. For those who prefer to treat complex numbers and quadratic equations with a negative discriminant early, Section 5.3 can be covered any time after Section 1.3.

Chapter 2: Linear and Quadratic Functions

This chapter provides an introduction to functions and then discusses two specific types of functions: linear functions and quadratic functions, along with models that utilize these functions.

Chapter 3: Functions and Their Graphs

Perhaps the most important chapter. Section 3.6 can be skipped without adverse effects.

Chapter 4: Polynomial and Rational Functions

Topic selection is dependent on your syllabus.

Chapter 5: The Zeros of a Polynomial Function

Topic selection is dependent on your syllabus. Section 5.1 is not absolutely necessary, but its coverage makes some computation easier.

Chapter 6: Exponential and Logarithmic Functions

Sections 6.1-6.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.

Chapter 7: Systems of Equations and Inequalities

Sections 7.1-7.2 follow in sequence; Sections 7.3-7.7 require Sections 7.1 and 7.2, and may be covered in any order.

Chapter 8: Sequences; Induction; The Binomial Theorem

There are three independent parts: (1) Sections 8.1-8.3; (2) Section 8.4; (3) Section 8.5

Chapter 9: Counting and Probability

Sections 9.1-9.4 follow in order.

Chapter 10: Analytic Geometry Sections

10.1-10.4 follow in sequence. Section 10.5 is dependent on Sections 10.1-10.4 as well as Sections 7.1-7.2.