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More About This Textbook
Overview
Michael Sullivan’s timetested 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 Serieshas evolved to meet today’s course needs by integrating the usage of graphing calculator, activelearning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.
Product Details
Meet 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 a home in Oak Lawn IL and a condo in Naples FL.
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, twelve with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.
Mike has four children: Kathleen, who teaches college mathematics; Michael III, who also teaches college mathematics, and who is his coauthor on two precalculus series; Dan, who is a sales director for Pearson Education; and Colleen, who teaches middleschool 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 coauthor 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
R. Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
1. Graphs, Equations, and Inequalities
1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
1.3 Quadratic Equations
1.4 Complex Numbers; Quadratic Equations in the Complex Number System
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
1.7 Solving Inequalities
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
2. Graphs
2.1 Intercepts; Symmetry; Graphing Key Equations
2.2 Lines
2.3 Circles
2.4 Variation
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
3. Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewisedefined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
4. Linear and Quadratic Functions
4.1 Linear Functions, Their Properties, and Linear Models
4.2 Building Linear Models from Data
4.3 Quadratic Functions and Their Properties
4.4 Building Quadratic Models from Verbal Descriptions and Data
4.5 Inequalities Involving Quadratic Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
5. Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 The Real Zeros of a Polynomial Function
5.3 Properties of Rational Functions
5.4 The Graph of a Rational Function
5.5 Polynomial and Rational Inequalities
5.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 OnetoOne Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
7. Analytic Geometry
7.1 Conics
7.2 The Parabola
7.3 The Ellipse
7.4 The Hyperbola
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination
8.2 Systems of Linear Equations: Matrices
8.3 Systems of Linear Equations: Determinants
8.4 Matrix Algebra
8.5 Partial Fraction Decomposition
8.6 Systems of Nonlinear Equations
8.7 Systems of Inequalities
8.8 Linear Programming
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
9. Sequences; Induction; the Binomial Theorem
9.1 Sequences
9.2 Arithmetic Sequences
9.3 Geometric Sequences; Geometric Series
9.4 Mathematical Induction
9.5 The Binomial Theorem
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
10. Counting and Probability
10.1 Counting
10.2 Permutations and Combinations
10.3 Probability
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
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 coauthor 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, studentfriendly 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 broadbased 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
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 quadraticinform 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
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 "justintime" 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 6.16.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.
Chapter 7: Systems of Equations and Inequalities
Sections 7.17.2 follow in sequence; Sections 7.37.7 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 8.18.3; (2) Section 8.4; (3) Section 8.5
Chapter 9: Counting and Probability
Sections 9.19.4 follow in order.
Chapter 10: Analytic Geometry Sections
10.110.4 follow in sequence. Section 10.5 is dependent on Sections 10.110.4 as well as Sections 7.17.2.