College Algebra

About our authors Marvin Bittinger has taught math at the university level for more than 38 years, and he is now Professor Emeritus of mathematics education at Indiana University - Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra & trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” In addition, he also has an interest in philosophy and theology, particularly apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 granddaughters. Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels, with many years of developmental math and precalculus teaching experience at Indiana University - Purdue University Indianapolis. In addition to her career in textbook publishing she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children’s camp. David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael’s College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two-Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor’s degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts - Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has 2 sons, Monroe and Zachary. Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University - Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.

Graphs, Functions, and Models

1.1. Introduction to Graphing

Visualizing the Graph


1.2. Functions and Graphs
1.3. Linear Functions, Slope, and Applications

Visualizing the Graph
Mid-Chapter Mixed Review


1.4. Equations of Lines and Modeling
1.5. Linear Equations, Functions, Zeros, and Applications
1.6. Solving Linear Inequalities
Summary and Review
Review Exercises
Chapter Test


More on Functions

2.1. Increasing, Decreasing, and Piecewise Functions; Applications
2.2. The Algebra of Functions
2.3. The Composition of Functions

Mid-Chapter Mixed Review


2.4. Symmetry
2.5. Transformations

Visualizing the Graph


2.6. Variation and Applications
Summary and Review
Review Exercises
Chapter Test


Quadratic Functions and Equations; Inequalities

3.1. The Complex Numbers
3.2. Quadratic Equations, Functions, Zeros, and Models
3.3. Analyzing Graphs of Quadratic Functions

Visualizing the Graph
Mid-Chapter Mixed Review


3.4. Solving Rational Equations and Radical Equations
3.5. Solving Equations and Inequalities with Absolute Value

Summary and Review
Review Exercises
Chapter Test




Polynomial Functions and Rational Functions

4.1. Polynomial Functions and Modeling
4.2. Graphing Polynomial Functions

Visualizing the Graph


4.3. Polynomial Division; The Remainder Theorem and the Factor Theorem

Mid-Chapter Mixed Review


4.4. Theorems about Zeros of Polynomial Functions
4.5. Rational Functions

Visualizing the Graph


4.6. Polynomial Inequalities and Rational Inequalities

Study Guide
Review Exercises
Chapter Test




Exponential Functions and Logarithmic Functions

5.1. Inverse Functions
5.2. Exponential Functions and Graphs
5.3. Logarithmic Functions and Graphs

Visualizing the Graph
Mid-Chapter Mixed Review


5.4. Properties of Logarithmic Functions
5.5. Solving Exponential Equations and Logarithmic Equations
5.6. Applications and Models: Growth and Decay; Compound Interest 364

Study Guide
Review Exercises
Chapter Test




Systems of Equations and Matrices

6.1. Systems of Equations in Two Variables

Visualizing the Graph


6.2. Systems of Equations in Three Variables
6.3. Matrices and Systems of Equations
6.4. Matrix Operations

Mid-Chapter Mixed Review


6.5. Inverses of Matrices
6.6. Determinants and Cramer’s Rule
6.7. Systems of Inequalities and Linear Programming
6.8. Partial Fractions

Study Guide
Review Exercises
Chapter Test




Conic Sections

7.1. The Parabola
7.2. The Circle and the Ellipse

Mid-Chapter Mixed Review


7.3. The Hyperbola
7.4. Nonlinear Systems of Equations and Inequalities

Visualizing the Graph
Study Guide
Review Exercises
Chapter Test




Sequences, Series, and Combinatorics

8.1. Sequences and Series
8.2. Arithmetic Sequences and Series
8.3. Geometric Sequences and Series

Visualizing the Graph


8.4. Mathematical Induction

Mid-Chapter Mixed Review


8.5. Combinatorics: Permutations
8.6. Combinatorics: Combinations
8.7. The Binomial Theorem
8.8. Probability

Study Guide
Review Exercises
Chapter Test





Photo Credits Answers Additional Instructor’s Answers Index Index of Applications