# College Algebra

**by**Ratti, J. S.; McWaters, Marcus S.

### 9780321640314

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## Summary

## Author Biography

**J.S.Ratti **has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the "Center for Mathematical Services" at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and known as the coauthor of a successful finite mathematics textbook.

**Marcus McWaters **is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last *eleven* years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.

## Table of Contents

**P. Basic Concepts of Algebra**

P.1 The Real Numbers and Their Properties

P.2 Integer Exponents and Scientific Notation

P.3 Polynomials

P.4 Factoring Polynomials

P.5 Rational Expressions

P.6 Rational Exponents and Radicals

P.7 Topics in Geometry

Chapter P Summary

Chapter P Review Exercises

Chapter P Practice Test

**1. Equations and Inequalities**

1.1 Linear Equations in One Variable

1.2 Applications of Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Solving Other Types of Equations

1.6 Linear Inequalities

1.7 Equations and Inequalities Involving Absolute Value

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Practice Test A

Chapter 1 Practice Test B

**2. Graphs and Functions**

2.1 The Coordinate Plane

2.2 Graphs of Equations

2.3 Lines

2.4 Relations and Functions

2.5 Properties of Functions

2.6 A Library of Functions

2.7 Transformations of Functions

2.8 Combining Functions; Composite Functions

2.9 Inverse Functions

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Practice Test A

Chapter 2 Practice Test B

Cumulative Review Chapters P—2

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions

3.3 Dividing Polynomials

3.4 The Real Zeros of a Polynomial Function

3.5 The Complex Zeros of a Polynomial Function

3.6 Rational Functions

3.7 Polynomial and Rational Inequalities

3.8 Variation

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test A

Chapter 3 Practice Test B

Cumulative Review Chapters P—3

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 The Natural Exponential Function

4.3 Logarithmic Functions

4.4 Rules of Logarithms

4.5 Exponential and Logarithmic Equations

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test A

Chapter 4 Practice Test B

Cumulative Review Chapters P—4

**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 Systems of Nonlinear Equations

5.4 Systems of Inequalities

5.5 Linear Programming

5.6 Partial-Fraction Decomposition

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test A

Chapter 5 Practice Test B

Cumulative Review Chapters P—5

**6. Matrices and Determinants**

6.1 Matrices and Systems of Equations

6.2 Matrix Algebra

6.3 The Matrix Inverse

6.4 Determinants and Cramer's Rule

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test A

Chapter 6 Practice Test B

Cumulative Review Chapters P—6

**7. Conic Sections**

7.1 Conic Sections: Overview

7.2 The Parabola

7.3 The Ellipse

7.4 The Hyperbola

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test A

Chapter 7 Practice Test B

Cumulative Review Chapters P—7

**8. Further Topics in Algebra**

8.1 Sequences and Series

8.2 Arithmetic Sequences; Partial Sums

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles

8.7 Probability

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test A

Chapter 8 Practice Test B

Cumulative Review Chapters P—8

Answers to Selected Exercises

Credits

Index of Applications

Index