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## Summary

## Author Biography

**Mark Dugopolski** was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an M.S. in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign—Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

## Table of Contents

**P. Prerequisites**

P.1 Real Numbers and Their Properties

P.2 Integral Exponents and Scientific Notations

P.3 Rational Exponents and Radicals

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

P.7 Complex Numbers

Chapter P Highlights

Chapter P Review Exercises

Chapter P Test

**1. Equations, Inequalities, and Modeling**

1.1 Equations in One Variable

1.2 Constructing Models to Solve Problems

1.3 Equations and Graphs in Two Variables

1.4 Linear Equations in Two Variables

1.5 Scatter Diagrams and Curve Fitting

1.6 Quadratic Equations

1.7 Linear and Absolute Value Inequalities

Chapter 1 Highlights

Chapter 1 Review Exercises

Chapter 1 Test

Tying it all Together

**2. Functions and Graphs**

2.1 Functions

2.2 Graphs of Relations and Functions

2.3 Families of Functions, Transformations, and Symmetry

2.4 Operations with Functions

2.5 Inverse Functions

2.6 Constructing Functions with Variation

Chapter 2 Highlights

Chapter 2 Review Exercises

Chapter 2 Test

Tying it all Together

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions and Inequalities

3.2 Zeros of Polynomial Functions

3.3 The Theory of Equations

3.4 Miscellaneous Equations

3.5 Graphs of Polynomial Functions

3.6 Rational Functions and Inequalities

Chapter 3 Highlights

Chapter 3 Review Exercises

Chapter 3 Test

Tying it all Together

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions and Their Applications

4.2 Logarithmic Functions and Their Applications

4.3 Rules of Logarithms

4.4 More Equations and Applications

Chapter 4 Highlights

Chapter 4 Review Exercises

Chapter 4 Test

Tying it all Together

**5. Systems of Equations and Inequalities**

5.1 Systems of Linear Equations in Two Variables

5.2 Systems of Linear Equations in Three Variables

5.3 Nonlinear Systems of Equations

5.4 Partial Fractions

5.5 Inequalities and Systems of Inequalities in Two Variables

5.6 The Linear Programming Model

Chapter 5 Highlights

Chapter 5 Review Exercises

Chapter 5 Test

Tying it all Together

**6. Matrices and Determinants**

6.1 Solving Linear Systems Using Matrices

6.2 Operations with Matrices

6.3 Multiplication of Matrices

6.4 Inverses of Matrices

6.5 Solutions of Linear Systems in Two Variables Using Determinants

6.6 Solutions of Linear Systems in Three Variables Using Determinants

Chapter 6 Highlights

Chapter 6 Review Exercises

Chapter 6 Test

Tying it all Together

**7. The Conic Sections**

7.1 The Parabola

7.2 The Ellipse and the Circle

7.3 The Hyperbola

Chapter 7 Highlights

Chapter 7 Review Exercises

Chapter 7 Test

Tying it all Together

**8. Sequences, Series, and Probability**

8.1 Sequences

8.2 Series

8.3 Geometric Sequences and Series

8.4 Counting and Permutations

8.5 Combinations, Labeling, and the Binomial Theorem

8.6 Probability

8.7 Mathematical Induction

Chapter 8 Highlights

Chapter 8 Review Exercises

Chapter 8 Test

Appendix: Solutions to Try This Exercises

Answers to All Exercises

Credits

Index of Applications

Index