College Algebra

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall.

Preface

Acknowledgments

To the Student

About the Author

Applications Index

 

P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

            Mid-Chapter Check Point

P.5 Factoring Polynomials

P.6 Rational Expressions

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER P TEST

 

1. Equations and Inequalities

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

            Mid-Chapter Check Point

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 1 TEST

 

2. Functions and Graphs

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

            Mid-Chapter Check Point

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 2 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)

 

3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

            Mid-Chapter Check Point

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 3 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3)

 

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

            Mid-Chapter Check Point

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 4 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)

 

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 Partial Fractions

5.4 Systems of Nonlinear Equations in Two Variables

            Mid-Chapter Check Point

5.5 Systems of Inequalities

5.6 Linear Programming

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 5 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)

 

6. Matrices and Determinants

6.1 Matrix Solutions to Linear Systems

6.2 Inconsistent and Dependent Systems and Their Applications

6.3 Matrix Operations and Their Applications

            Mid-Chapter Check Point

6.4 Multiplicative Inverses of Matrices and Matrix Equations

6.5 Determinants and Cramer's Rule

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 6 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6)

 

7. Conic Sections

7.1 The Ellipse

7.2 The Hyperbola

            Mid-Chapter Check Point

7.3 The Parabola

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 7 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-7)

 

8. Sequences, Induction, and Probability

8.1 Sequences and Summation Notation

8.2 Arithmetic Sequences

8.3 Geometric Sequences and Series

            Mid-Chapter Check Point

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles, Permutations, and Combinations

8.7 Probability

            SUMMARY, REVIEW, AND TEST

            REVIEW EXERCISES

            CHAPTER 8 TEST

            CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-8)

 

Appendix A: Where Did That Come From?

Selected Proofs

Answers to Selected Exercises

Subject Index

Photo Credits