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. Review of the Real Number System

R.1 Basic Concepts

R.2 Operations on Real Numbers

R.3 Exponents, Roots, and Order of Operations

R.4 Properties of Real Numbers

            Chapter R Summary

            Chapter R Test

            Study Skills: Reading Your Math Textbook

1. Linear Equations, Inequalities, and Applications

1.1 Linear Equations in One Variable

            Study Skills: Completing Your Homework

1.2 Formulas and Percent

            Study Skills: Taking Lecture Notes

1.3 Applications of Linear Equations

1.4 Further Applications of Linear Equations

            Summary Exercises: Applying Problem-Solving Techniques

1.5 Linear Inequalities in One Variable

            Study Skills: Using Study Cards

1.6 Set Operations and Compound Inequalities

            Study Skills: Using Study Cards Revisited

1.7 Absolute Value Equations and Inequalities

            Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities

            Study Skills: Reviewing a Chapter

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Mixed Review Exercises

            Chapter 1 Test

2. Linear Equations, Graphs, and Functions

2.1 Linear Equations in Two Variables

            Study Skills: Managing Your Time

2.2 The Slope of a Line

2.3 Writing Equations of Lines

            Study Skills: Taking Math Tests

            Summary Exercises: Finding Slopes and Equations of Lines

2.4 Linear Inequalities in Two Variables

2.5 Introduction to Relations and Functions

            Study Skills: Analyzing Your Test Results

2.6 Function Notation and Linear Functions

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Mixed Review Exercises

            Chapter 2 Test

            Chapters R—2 Cumulative Review Exercises

3. Systems of Linear Equations

3.1 Systems of Linear Equations in Two Variables

            Study Skills: Preparing for Your Math Final Exam

3.2 Systems of Linear Equations in Three Variables

3.3 Applications of Systems of Linear Equations

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Mixed Review Exercises

            Chapter 3 Test

            Chapters R—3 Cumulative Review Exercises

4. Exponents, Polynomials, and Polynomial Functions

4.1 Integer Exponents and Scientific Notation

4.2 Adding and Subtracting Polynomials

4.3 Polynomial Functions, Graphs, and Composition

4.4 Multiplying Polynomials

4.5 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

5.1 Greatest Common Factors and Factoring by Grouping

5.2 Factoring Trinomials

5.3 Special Factoring

5.4 A General Approach to Factoring

5.5 Solving Equations by the Zero-Factor Property

            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 Functions

6.1 Rational Expressions and Functions; Multiplying and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Fractions

6.4 Equations with Rational Expressions and Graphs

            Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations

6.5 Applications of Rational Expressions

6.6 Variation

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Mixed Review Exercises

            Chapter 6 Test

            Chapters R—6 Cumulative Review Exercises

7. Roots, Radicals, and Root Functions

7.1 Radical Expressions and Graphs

7.2 Rational Exponents

7.3 Simplifying Radicals, the Distance Formula, and Circles

7.4 Adding and Subtracting Radical Expressions

7.5 Multiplying and Dividing Radical Expressions

            Summary Exercises: Performing Operations with Radicals and Rational Exponents

7.6 Solving Equations with Radicals

7.7 Complex Numbers

            Chapter 7 Summary

            Chapter 7 Review Exercises

            Chapter 7 Mixed Review Exercises

            Chapter 7 Test

            Chapters R—7 Cumulative Review Exercises

8. Quadratic Equations, Inequalities, and Functions

8.1 The Square Root Property and Completing the Square

8.2 The Quadratic Formula

8.3 Equations Quadratic in Form

            Summary Exercises: Applying Methods for Solving Quadratic Equations

8.4 Formulas and Further Applications

8.5 Graphs of Quadratic Functions

8.6 More about Parabolas and Their Applications

8.7 Polynomial and Rational Inequalities

            Chapter 8 Summary

            Chapter 8 Review Exercises

            Chapter 8 Mixed Review Exercises

            Chapter 8 Test

            Chapters R—8 Cumulative Review Exercises

9. Inverse, Exponential, and Logarithmic Functions

9.1 Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Common and Natural Logarithms

9.6 Exponential and Logarithmic Equations;

Further Applications

            Chapter 9 Summary

            Chapter 9 Review Exercises

            Chapter 9 Mixed Review Exercises

            Chapter 9 Test

            Chapters R—9 Cumulative Review Exercises

Appendix: Synthetic Division

Answers to Selected Exercises

Glossary

Credits

Index

Additional topics available in MyMathLab: Solving Systems of Linear Equations by Matrix Methods; Determinants and Cramer’s Rule; 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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