College Algebra

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 retiring recently. 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 s a full-time professor at Joliet Jr. College with training in mathematics, statistics, and economics. Built from experience in the classroom using feedback from his students Mike has numerous Pearson textbooks in publication including a Developmental Math series and two Precalculus series and a statistics series. When not in the classroom or writing, you’ll find Mike trying to sneak in a round of golf if the schedules of his three children: Michael, Kevin, and Marissa allow it. Which might be a little easier now that Michael and Kevin are both in college. 

F. Foundations: A Prelude to Functions

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

F.3 Lines

F.4 Circles

 

1. Functions and Their Graphs

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise-defined Functions

1.5 Graphing Techniques: Transformations

1.6 Mathematical Models: Constructing Functions

1.7 Building Mathematical Models Using Variation

        Chapter Review

        Chapter Test

        Chapter Projects

 

2. Linear and Quadratic Functions

2.1 Properties of Linear Functions and Linear Models

2.2 Building Linear Models from Data

2.3 Quadratic Functions and Their Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Building Quadratic Models from Verbal Descriptions and from Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

3. Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 The Real Zeros of a Polynomial Function

3.3 Complex Zeros; Fundamental Theorem of Algebra

3.4 Properties of Rational Functions

3.5 The Graph of a Rational Function

3.6 Polynomial and Rational Inequalities

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

4. Exponential and Logarithmic Functions

4.1 Composite Functions

4.2 One-to-One Functions; Inverse Functions

4.3 Exponential Functions

4.4 Logarithmic Functions

4.5 Properties of Logarithms

4.6 Logarithmic and Exponential Equations

4.7 Compound Interest

4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

5. Conics

5.1 Conics

5.2 The Parabola

5.3 The Ellipse

5.4 The Hyperbola

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

6. Systems of Equations and Inequalities

6.1 Systems of Linear Equations: Substitution and Elimination

6.2 Systems of Linear Equations: Matrices

6.3 Systems of Linear Equations: Determinants

6.4 Matrix Algebra

6.5 Partial Fraction Decomposition

6.6 Systems of Nonlinear Equations

6.7 Systems of Inequalities

6.8 Linear Programming

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

7. Sequences; Induction; the Binomial Theorem

7.1 Sequences

7.2 Arithmetic Sequences

7.3 Geometric Sequences; Geometric Series

7.4 Mathematical Induction

7.5 The Binomial Theorem

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

8. Counting and Probability

8.1 Counting

8.2 Permutations and Combinations

8.3 Probability

        Chapter Review

        Chapter Test

        Chapter Projects

        Cumulative Review

 

Appendix A. Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Factoring Polynomials

A.5 Synthetic Division

A.6 Rational Expressions

A.7 nth Roots; Rational Exponents

A.8 Solving Equations

A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

A.10 Interval Notation; Solving Inequalities

A.11 Complex Numbers

 

Appendix B. Graphing Utilities

B.1 The Viewing Rectangle

B.2 Using a Graphing Utility to Graph Equations

B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

B.4 Using a Graphing Utility to Solve Equations

B.5 Square Screens

B.6 Using a Graphing Utility to Graph Inequalities

B.7 Using a Graphing Utility to Solve Systems of Linear Equations

B.8 Using a Graphing Utility to Graph a Polar Equation

B.9 Using a Graphing Utility to Graph Parametric Equations

 

Answers

Index