College Algebra

Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years. He is a native of Chicago’s South Side and currently resides in Oaklawn.  Mike has four children.  The two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project.  Mike III co-authored the Sullivan Graphing with Data Analysis series as well as this series.  Dan, the youngest, sells for Prentice Hall as a generalist.   Mike has authored or co-authored over ten books.  He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oaklawn, where Mike enjoys gardening.  Mike first signed this series with Deleen Publishing (Acquired by Macmillan) in 1985.   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.   Why We Wrote the Book:   Work on this series began with a unique perspective.  Teaching at a large urban institution and a smaller two-year college has allowed us to see firsthand the challenges associated with teaching students with diverse backgrounds in an urban setting.  Successful textbooks must be accessible to students.  As lead author of this series, one of the most important things I bring to the project is my experience as author of a successful calculus text.  Mike and I are both aware that students must be prepared in a Precalculus course for subsequent mathematics courses.  We also realize that many College Algebra students will not be going on to take upper level math courses.  In this series we resolved the seeming dilemma without sacrificing accessibility.   The books in this series are designed to be mathematically comprehensive and to provide substantial mathematical preparation for subsequent courses.  At the same time, great effort has been expended to motivate the material and to make it accessible to even poorly prepared students.

FOUNDATIONS: A PRELUDE TO FUNCTIONS

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations; Intercepts; Symmetry

F.3 Lines

F.4 Circles

 

Chapter 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

Chapter Review

Chapter Test

Chapter Projects

 

Chapter 2 Linear and Quadratic Functions

2.1 Properties of Linear Functions

2.2 Building Linear Functions from Data; Direct Variation

2.3 Quadratic Functions and Their Real Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Quadratic Models; Building Quadratic Functions 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

 

 

Chapter 3       Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 Properties of Rational Functions

3.3 The Graph of a Rational Function; Inverse and Joint Variation

3.4 Polynomial and Rational Inequalities

3.5 The Real Zeros of a Polynomial Function

3.6 Complex Zeros: Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

 

Chapter 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 Project

Cumulative Review

 

Chapter 5       Analytic Geometry

5.1 Conics

5.2 The Parabola

5.3 The Ellipse

5.4 The Hyperbola

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 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

 

Chapter 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

 

Chapter 8       Counting and Probability

8.1 Sets and Counting

8.2 Permutations and Combinations

8.3 Probability

Chapter Review

Chapter Test

Chapter Project

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 Algebraically

A.9 Interval Notation; Solving Inequalities

A.10 Problem Solving: Applications of Linear Equations

A.11 Complex Numbers

 

Appendix B Graphing Utilities

B.1 The Viewing Rectangle

B.2 Graphing Equations in Two Variables

B.3 Locating Intercepts and Checking for Symmetry

B.4 Solving Equations Using a Graphing Utility

B.5 Square Screens

B.6 Graphing Inequalities in Two Variables

B.7 Solving Systems of Linear Equations

 

Answers

Index