Introductory & Intermediate Algebra

Marge Lial (late) 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, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing 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. 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.

• Table of Contents R. Prealgebra ReviewR.1 FractionsR.2 Decimals and PercentsStudy Skills Using Your Math Text The Real Number System 1.1 Exponents, Order of Operations, and Inequality Study Skills Taking Lecture Notes1.2 Variables, Expressions, and Equations Study Skills Reading Your Math Text1.3 Real Numbers and the Number Line Study Skills Using Study Cards1.4 Adding Real Numbers1.5 Subtracting Real Numbers Study Skills Completing Your Homework1.6 Multiplying and Dividing Real Numbers Summary Exercises Performing Operations with Real Numbers1.7 Properties of Real Numbers1.8 Simplifying Expressions Study Skills Reviewing a ChapterEquations, Inequalities, and Applications 2.1 The Addition Property of Equality Study Skills Managing Your Time2.2 The Multiplication Property of Equality2.3 More on Solving Linear Equations Study Skills Using Study Cards RevisitedSummary Exercises Applying Methods for Solving Linear Equations2.4 An Introduction to Applications of Linear Equations2.5 Formulas and Additional Applications from Geometry2.6 Ratio, Proportion, and Percent Summary Exercises Applying Problem-Solving Techniques2.7 Solving Linear Inequalities Study Skills Taking Math TestsGraphs of Linear Equations and Inequalities in Two Variables 3.1 Linear Equations and Rectangular Coordinates Study Skills Analyzing Your Test Results3.2 Graphing Linear Equations in Two Variables3.3 The Slope of a Line3.4 Slope-Intercept Form of a Linear Equation3.5 Point-Slope Form of a Linear Equation and Modeling Summary Exercises Applying Graphing andEquation-Writing Techniques for LinesStudy Skills Preparing for Your Math Final Exam3.6 Graphing Linear Inequalities in Two VariablesSystems of Linear Equations and Inequalities 4.1 Solving Systems of Linear Equations by Graphing4.2 Solving Systems of Linear Equations by Substitution4.3 Solving Systems of Linear Equations by Elimination Summary Exercises Applying Techniques for Solving Systems of Linear Equations4.4 Applications of Linear Systems4.5 Solving Systems of Linear InequalitiesExponents and Polynomials 5.1 The Product Rule and Power Rules for Exponents5.2 Integer Exponents and the Quotient Rule Summary Exercises Applying the Rules for Exponents5.3 An Application of Exponents: Scientific Notation5.4 Adding and Subtracting Polynomials5.5 Multiplying Polynomials5.6 Special Products5.7 Dividing a Polynomial by a Monomial5.8 Dividing a Polynomial by a PolynomialFactoring and Applications 6.1 Greatest Common Factors; Factor by Grouping6.2 Factoring Trinomials6.3 Factoring Trinomials by Grouping6.4 Factoring Trinomials Using the FOIL Method6.5 Special Factoring Techniques6.6 A General Approach to Factoring6.7 Solving Quadratic Equations Using the Zero-Factor Property6.8 Applications of Quadratic EquationsRational Expressions and Applications 7.1 The Fundamental Property of Rational Expressions7.2 Multiplying and Dividing Rational Expressions7.3 Least Common Denominators7.4 Adding and Subtracting Rational Expressions7.5 Complex Fractions7.6 Solving Equations with Rational Expressions Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations7.7 Applications of Rational Expressions7.8 VariationEquations, Inequalities, Graphs, and Systems Revisited 8.1 Review of Solving Linear Equations and Inequalities in one Variable8.2 Set Operations and Compound Inequalities8.3 Absolute Value Equations and Inequalities Summary Exercises Solving Linear and Absolute Value Equations and Inequalities8.4 Review of Graphing Linear Equations in Two Variables; Slope8.6 Systems of Linear Equations in Three Variables; ApplicationsRelations and Functions 9.1 Introduction to Relations and Functions9.2 Function Notation and Linear Functions9.3 Polynomial Functions, Operations, and Graphs9.4 VariationRoots, Radicals, and Root Functions 10.1 Radical Expressions and Graphs10.2 Rational Exponents10.3 Simplifying Radical Expressions10.4 Adding and Subtracting Radical Expressions10.5 Multiplying and Dividing Radical Expressions Summary Exercises Performing Operations with Radicals and Rational Exponents10.6 Solving Equations with Radicals10.7 Complex NumbersQuadratic Equations, Inequalities, and Functions 11.1 Solving Quadratic Equations by the Square Root Property11.2 Solving Quadratic Equations by Completing the Square11.3 Solving Quadratic Equations by the Quadratic Formula11.4 Equations Quadratic in Form Summary Exercises Applying Methods for Solving Quadratic Equations11.5 Formulas and Further Applications11.6 Graphs of Quadratic Functions11.7 More about Parabolas and Their Applications11.8 Polynomial and Rational InequalitiesInverse, Exponential, and Logarithmic Functions 12.1 Composition of Functions12.2 Inverse Functions12.3 Exponential Functions12.4 Logarithmic Functions12.5 Properties of Logarithms12.6 Common and Natural Logarithms12.7 Exponential and Logarithmic Equations and Their ApplicationsNonlinear Functions, Conic Sections, and Nonlinear Systems 13.1 Additional Graphs of Functions13.2 Circles and Ellipses13.3 Hyperbolas and Functions Defined by Radicals13.4 Nonlinear Systems of Equations13.5 Second-Degree Inequalities and Systems of InequalitiesAppendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra) Appendix B: Synthetic Division Appendix C: Solving Systems of Linear Equations by Matrix Methods Answers to Selected Exercises Index