Beginning and Intermediate Algebra

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Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series that includes Introductory Algebra, Intermediate Algebra, and Introductory and Intermediate Algebra. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.

Preface

            Study Skills: Using Your Math Textbook

R. Prealgebra Review

R.1 Fractions

R.2 Decimals and Percents

            Study Skills: Reading Your Math Textbook

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality

            Study Skills: Taking Lecture Notes

1.2 Variables, Expressions, and Equations

1.3 Real Numbers and the Number Line

            Study Skills: Completing Your Homework

1.4 Adding and Subtracting Real Numbers

            Study Skills: Using Study Cards

1.5 Multiplying and Dividing Real Numbers

            Summary Exercises: Performing Operations with Real Numbers

1.6 Properties of Real Numbers

1.7 Simplifying Expressions

            Study Skills: Reviewing a Chapter

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Mixed Review Exercises

            Chapter 1 Test

2. Linear Equations and Inequalities in One Variable

2.1 The Addition Property of Equality

            Study Skills: Managing Your Time

2.2 The Multiplication Property of Equality

2.3 More on Solving Linear Equations

            Study Skills: Using Study Cards Revisited

            Summary Exercises: Applying Methods for Solving Linear Equations

2.4 Applications of Linear Equations

2.5 Formulas and Additional Applications from Geometry

2.6 Ratio, Proportion, and Percent

2.7 Further Applications of Linear Equations

2.8 Solving Linear Inequalities

            Study Skills: Taking Math Tests

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Mixed Review Exercises

            Chapter 2 Test

            Chapters R—2 Cumulative Review Exercises

3. Linear Equations and Inequalities in Two Variables

3.1 Linear Equations and Rectangular Coordinates

            Study Skills: Analyzing Your Test Results

3.2 Graphing Linear Equations in Two Variables

3.3 The Slope of a Line

            Study Skills: Preparing for Your Math Final Exam

3.4 Slope-Intercept Form of a Linear Equation

3.5 Point-Slope Form of a Linear Equation and Modeling

            Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Mixed Review Exercises

            Chapter 3 Test

            Chapters R—3 Cumulative Review Exercises

4. Exponents and Polynomials

4.1 The Product Rule and Power Rules for Exponents

4.2 Integer Exponents and the Quotient Rule

            Summary Exercises: Applying the Rules for Exponents

4.3 Scientific Notation

4.4 Adding, Subtracting, and Graphing Polynomials

4.5 Multiplying Polynomials

4.6 Special Products

4.7 Dividing Polynomials

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Mixed Review Exercises

            Chapter 4 Test

            Chapters R—4 Cumulative Review Exercises

5. Factoring and Applications

5.1 The Greatest Common Factor; Factoring by Grouping

5.2 Factoring Trinomials

5.3 More on Factoring Trinomials

5.4 Special Factoring Techniques

            Summary Exercises: Recognizing and Applying Factoring Strategies

5.5 Solving Quadratic Equations Using the Zero-Factor Property

5.6 Applications of Quadratic Equations

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Mixed Review Exercises

            Chapter 5 Test

            Chapters R—5 Cumulative Review Exercises

6. Rational Expressions and Applications

6.1 The Fundamental Property of Rational Expressions

6.2 Multiplying and Dividing Rational Expressions

6.3 Least Common Denominators

6.4 Adding and Subtracting Rational Expressions

6.5 Complex Fractions

6.6 Solving Equations with Rational Expressions

            Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations

6.7 Applications of Rational Expressions

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Mixed Review Exercises

            Chapter 6 Test

            Chapters R—6 Cumulative Review Exercises

7. Graphs, Linear Equations, and Systems

7.1 Review of Graphs and Slopes of Lines

7.2 Review of Equations of Lines; Linear Models

7.3 Solving Systems of Linear Equations by Graphing

7.4 Solving Systems of Linear Equations by Substitution

7.5 Solving Systems of Linear Equations by Elimination

            Summary Exercises: Applying Techniques for Solving Systems of Linear Equations

7.6 Systems of Linear Equations in Three Variables

7.7 Applications of Systems of Linear Equations

            Chapter 7 Summary

            Chapter 7 Review Exercises

            Chapter 7 Mixed Review Exercises

            Chapter 7 Test

            Chapters R—7 Cumulative Review Exercises

8. Inequalities and Absolute Value

8.1 Review of Linear Inequalities in One Variable

8.2 Set Operations and Compound Inequalities

8.3 Absolute Value Equations and Inequalities

            Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities

8.4 Linear Inequalities and Systems in Two Variables

            Chapter 8 Summary

            Chapter 8 Review Exercises

            Chapter 8 Mixed Review Exercises

            Chapter 8 Test

            Chapters R—8 Cumulative Review Exercises

9. Relations and Functions

9.1 Introduction to Relations and Functions

9.2 Function Notation and Linear Functions

9.3 Polynomial Functions, Operations, and Composition

9.4 Variation

            Chapter 9 Summary

            Chapter 9 Review Exercises

            Chapter 9 Mixed Review Exercises

            Chapter 9 Test

            Chapters R—9 Cumulative Review Exercises

10. Roots, Radicals, and Root Functions

10.1 Radical Expressions and Graphs

10.2 Rational Exponents

10.3 Simplifying Radicals, the Distance Formula, and Circles

10.4 Adding and Subtracting Radical Expressions

10.5 Multiplying and Dividing Radical Expressions

            Summary Exercises: Performing Operations with Radicals and Rational Exponents

10.6 Solving Equations with Radicals

10.7 Complex Numbers

            Chapter 10 Summary

            Chapter 10 Review Exercises

            Chapter 10 Mixed Review Exercises

            Chapter 10 Test

            Chapters R—10 Cumulative Review Exercises

11. Quadratic Equations, Inequalities, and Functions

11.1 Solving Quadratic Equations by the Square Root Property

11.2 Solving Quadratic Equations by Completing the Square

11.3 Solving Quadratic Equations by the Quadratic Formula

11.4 Solving Equations Quadratic in Form

            Summary Exercises: Applying Methods for Solving Quadratic Equations

11.5 Formulas and Further Applications

11.6 Graphs of Quadratic Functions

11.7 More about Parabolas and Their Applications

11.8 Polynomial and Rational Inequalities

            Chapter 11 Summary

            Chapter 11 Review Exercises

            Chapter 11 Mixed Review Exercises

            Chapter 11 Test

            Chapters R—11 Cumulative Review Exercises

12. Inverse, Exponential, and Logarithmic Functions

12.1 Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Common and Natural Logarithms

12.6 Exponential and Logarithmic Equations; Further Applications

            Chapter 12 Summary

            Chapter 12 Review Exercises

            Chapter 12 Mixed Review Exercises

            Chapter 12 Test

            Chapters R—12 Cumulative Review Exercises

Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Beginning to Intermediate Algebra)

Appendix B: Synthetic Division

Answers to Selected Exercises

Glossary

Credits

Index

Additional topics available in MyMathLab: Sets; Introduction to Calculators; Solving Systems of Linear Equations by Matrix Methods; Piecewise Linear Functions; Conic Sections; Nonlinear Systems of Equations; Second-Degree Inequalities and Systems of Inequalities; Linear Programming; Sequences and Series; The Binomial Theorem

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