Algebra for College Students

About our authors The late 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, 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 25 years of teaching at the high school and university levels and 15 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 2 sons, Andrew and Tyler.

• Study Skill 1: Using Your Math TextStudy Skill 2: Reading Your Math TextStudy Skill 3: Taking Lecture NotesStudy Skill 4: Completing Your HomeworkStudy Skill 5: Using Study CardsStudy Skill 6: Managing Your TimeStudy Skill 7: Reviewing a ChapterStudy Skill 8: Taking Math TestsStudy Skill 9: Analyzing Your Test ResultsStudy Skill 10: Preparing for Your Math Final Review of the Real Number System R.1 Fractions, Decimals, and PercentsR.2 Basic Concepts from AlgebraR.3 Operations on Real NumbersR.3 Exponents, Roots, and Order of OperationsR.4 Properties of Real NumbersChapter R SummaryChapter R TestLinear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable1.2 Formulas and Percent1.3 Applications of Linear Equations1.4 Further Applications of Linear Equations Summary Exercises: Applying Problem-Solving Techniques1.5 Linear Inequalities in One Variable1.6 Set Operations and Compound Inequalities1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and InequalitiesStudy Skills: Reviewing a ChapterChapter 1 SummaryChapter 1 Review ExercisesChapter 1 Mixed Review ExercisesChapter 1 TestChapters R and 1 Cumulative Review ExercisesLinear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables2.2 The Slope of a Line2.3 Writing Equations of Lines Summary Exercises: Finding Slopes and Equations of Lines2.4 Linear Inequalities in Two Variables2.5 Introduction to Relations and Functions2.6 Function Notation and Linear FunctionsChapter 2 SummaryChapter 2 Review ExercisesChapter 2 Mixed Review ExercisesChapter 2 TestChapters R—2 Cumulative Review ExercisesSystems of Linear Equations 3.1 Systems of Linear Equations in Two Variables3.2 Systems of Linear Equations in Three Variables3.3 Applications of Systems of Linear EquationsChapter 3 SummaryChapter 3 Review ExercisesChapter 3 Mixed Review ExercisesChapter 3 TestChapters R–3 Cumulative Review ExercisesExponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents and Scientific Notation4.2 Adding and Subtracting Polynomials4.3 Polynomial Functions, Graphs, and Composition4.4 Multiplying Polynomials4.5 Dividing PolynomialsChapter 4 SummaryChapter 4 Review ExercisesChapter 4 Mixed Review ExercisesChapter 4 TestChapters R–4 Cumulative Review ExercisesFactoring 5.1 Greatest Common Factors and Factoring by Grouping5.2 Factoring Trinomials5.3 Special Factoring5.4 A General Approach to Factoring5.5 Solving Equations by the Zero-Factor PropertyChapter 5 SummaryChapter 5 Review ExercisesChapter 5 Mixed Review ExercisesChapter 5 TestChapters R–5 Cumulative Review ExercisesRational Expressions and Functions 6.1 Rational Expressions and Functions; Multiplying and Dividing6.2 Adding and Subtracting Rational Expressions6.3 Complex Fractions6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations6.5 Applications of Rational Expressions6.6 VariationChapter 6 SummaryChapter 6 Review ExercisesChapter 6 Mixed Review ExercisesChapter 6 TestChapters R–6 Cumulative Review ExercisesRoots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs7.2 Rational Exponents7.3 Simplifying Radicals, the Distance Formula, and Circles7.4 Adding and Subtracting Radical Expressions7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents7.6 Solving Equations with Radicals7.7 Complex NumbersChapter 7 SummaryChapter 7 Review ExercisesChapter 7 Mixed Review ExercisesChapter 7 TestChapters R–7 Cumulative Review ExercisesQuadratic Equations and Inequalities 8.1 The Square Root Property and Completing the Square8.2 The Quadratic Formula8.3 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations8.4 Formulas and Further Applications8.5 Polynomial and Rational InequalitiesChapter 8 SummaryChapter 8 Review ExercisesChapter 8 Mixed Review ExercisesChapter 8 TestChapters R–8 Cumulative Review ExercisesAdditional Graphs of Functions and Relations 9.1 Review of Operations and Composition9.2 Graphs of Quadratic Functions9.3 More About Parabolas and Their Applications9.4 Symmetry; Increasing and Decreasing Functions9.5 Piecewise Linear FunctionsChapter 9 SummaryChapter 9 Review ExercisesChapter 9 Mixed Review ExercisesChapter 9 TestChapters R–9 Cumulative Review ExercisesInverse, Exponential, and Logarithmic Functions 10.1 Inverse Functions10.2 Exponential Functions10.3 Logarithmic Functions10.4 Properties of Logarithms10.5 Common and Natural Logarithms10.6 Exponential and Logarithmic Equations; Further ApplicationsChapter 10 SummaryChapter 10 Review ExercisesChapter 10 Mixed Review ExercisesChapter 10 TestChapters R–10 Cumulative Review ExercisesPolynomial and Rational Functions 11.1 Zeros of Polynomial Functions (I)11.2 Zeros of Polynomial Functions (II)11.3 Graphs and Applications of Polynomial Functions Summary Exercises: Examining Polynomial Functions and Graphs11.4 Graphs and Applications of Rational FunctionsChapter 11 SummaryChapter 11 Review ExercisesChapter 11 Mixed Review ExercisesChapter 11 TestChapters R–11 Cumulative Review ExercisesConic Sections and Nonlinear Systems 12.1 Circles Revisited and Ellipses12.2 Hyperbolas and Functions Defined by Radicals12.3 Nonlinear Systems of Equations12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear ProgrammingChapter 12 SummaryChapter 12 Review ExercisesChapter 12 Mixed Review ExercisesChapter 12 TestChapters R–12 Cumulative Review ExercisesFurther Topics in Algebra 13.1 Sequences and Series13.2 Arithmetic Sequences13.3 Geometric Sequences13.4 The Binomial Theorem13.5 Mathematical Induction13.6 Counting Theory13.7 Basics of ProbabilityChapter 13 SummaryChapter 13 Review ExercisesChapter 13 Mixed Review ExercisesChapter 13 TestChapters R–13 Cumulative Review ExercisesAppendices A. Solving Systems of Linear Equations by Matrix MethodsB. Determinants and Cramer’s RuleC. Properties of MatricesD. Matrix InversesPhoto CreditsAnswers to Selected ExercisesIndex