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## Summary

## Author Biography

An award-winning instructor and best-selling author, **Elayn Martin-Gay** has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for *Excellence in Teaching*, and *Outstanding Developmental Educator* at University of New Orleans, presented by the Louisiana Association of Developmental Educators.

Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the **Chapter Test Prep Video** to help students as they prepare for a test–their most “teachable moment!”

Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the **Instructor-to-Instructor** video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.

Her textbooks and acclaimed video program support Elayn's passion of helping

**every**student to succeed.

## Table of Contents

**Chapter 1 Real Numbers and Algebraic Expressions**

1.1 Tips for Success in Mathematics

1.2 Algebraic Expressions and Sets of Numbers

1.3 Equations, Inequalities, and Properties of Real Numbers

1.4 Operations on Real Numbers

1.5 Order of Operations and Algebraic Expressions

1.6 Exponents and Scientific Notation

1.7 More Work with Exponents and Scientific Notation

**Chapter 2 Equations, Inequalities, and Problem Solving**

2.1 Lienar Equations in One Variable

2.2 An Introduction to Problem Solving

2.3 Formulas and Problem Solving

2.4 Linear Inequalities and Problem Solving

2.5 Sets and Compound Inequalities

2.6 Absolute Value Equations

2.7 Absolute Value Inequalities

**Chapter 3 Graphs and Functions**

3.1 Graphing Linear Equations

3.2 The Slope of a Line

3.3 The Slope-Intercept Form

3.4 More Equations of Lines

3.5 Graphing Linear Inequalities

3.6 Introduction to Functions

3.7 Finding Domains and Ranges from Graphs and Graphing Piecewise-Defined Functions

3.8 Shifting and Reflecting Graphs of Functions

**Chapter 4 Systems of Equations and Inequalities**

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Systems of Linear Equations and Problem Solving

4.4 Solving Systems of Equations Using Matrices

4.5 Systems of Linear Inequalities

**Chapter 5 Polynomials and Polynomial Functions**

5.1 Polynomial Functions and Adding and Subtracting Polynomials

5.2 Multiplying Polynomials

5.3 Dividing Polynomials and Synthetic Division

5.4 The Greatest Common Factor and Factoring by Grouping

5.5 Factoring Trinomials

5.6 Factoring by Special Products

5.7 Solving Equations by Factoring and Solving Problems

**Chapter 6 Rational Expressions**

6.1 Rational Functions and Multiplying and Dividing Rational Expressoins

6.2 Adding and Subtracting Rational Expressions

6.3 Simplifying Complex Fractions

6.4 Solving Equations Containing Rational Expressions

6.5 Rational Equations and Problem Solving

6.6 Variation and Problem Solving** **

**Chapter 7 Rational Exponents, Radicals, and Complex Numbers**

7.1 Radical Expressions and Radical Functions

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Adding, Subtracting, and Multiplying Radical Expressions

7.5 Rationalizing Numerators and Denominators of Radical Expressions

7.6 Radical Equations and Problem Solving

7.7 Complex Numbers

**Chapter 8 Quadratic Equations and Functions**

8.1 Solving Quadratic Equations by Completing the Square

8.2 Solving Quadratic Equations by Using the Quadratic Formula

8.3 Solving Equations by Using Quadratic Methods

8.4 Nonlinear Inequalities in One Variable

8.5 Quadratic Functions and Their Graphs

8.6 Further Graphing of Quadratic Functions

** **

**Chapter 9 Exponential and Logarithmic Functions**

9.1 The Algebra of Functions

9.2 Inverse Functions

9.3 Exponential Functions

9.4 Exponential Growth and Decay Functions

9.5 Logarithmic Functions

9.6 Properties of Logarithms

9.7 Common Logarithms, Natural Logarithms, and Change of Base

9.8 Exponential and Logarithmic Equations and Problem Solving

**Chapter 10 Conic Sections **

10.1 The Parabola and the Circle

10.2 The Ellipse and the Hyperbola

10.3 Solving Nonlinear Systems of Equations

10.4 Nonlinear Inequalities and Systems of Inequalities

Appendix A Fractions

Appendix B Solving Systems of Equations Using Determinants

Appendic C An Introduction to Using a Graphing Utility

Appendix D Stretching and Compressing Graphs of Absolute Value Functions

Appendix E Review of Angles, Lines, and Special Triangles

Student Resources