Precalculus -- ACCUMULATOR

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. Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks where she earned a bachelor’s degree in Secondary Mathematics Education. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding. She is able to pursue these interests as a contributor on the Lial Developmental Math series, and a co-author on the Precalculus series.

• Table of Contents Review of Basic Concepts R-1 Fractions, Decimals, and PercentsR-2 Sets and Real NumbersR-3 Real Number Operations and PropertiesR-4 Integer and Rational ExponentsR-5 PolynomialsR-6 Factoring PolynomialsR-7 Rational ExpressionsR-8 Radical Expressions Equations and Inequalities 1-1 Linear Equations1-2 Applications and Modeling with Linear Equations1-3 Complex Numbers1-4 Quadratic Equations1-5 Applications and Modeling with Quadratic Equations1-6 Other Types of Equations and Applications1-7 Inequalities1-8 Absolute Value Equations and InequalitiesGraphs and Functions 2-1 Rectangular Coordinates and Graphs2-2 Circles2-3 Functions2-4 Linear Functions2-5 Equations of Lines and Linear Models2-6 Graphs of Basic Functions2-7 Graphing Techniques2-8 Function Operations and CompositionPolynomial and Rational Functions 3-1 Quadratic Functions and Models3-2 Synthetic Division3-3 Zeros of Polynomial Functions3-4 Polynomial Functions: Graphs, Applications, and Models3-5 Rational Functions: Graphs, Applications, and Models3-6 Polynomial and Rational Inequalities3-7 VariationInverse, Exponential, and Logarithmic Functions 4-1 Inverse Functions4-2 Exponential Functions4-3 Logarithmic Functions4-4 Evaluating Logarithms and the Change-of-Base Theorem4-5 Exponential and Logarithmic Equations4-6 Applications of Models of Exponential Growth and DecayTrigonometric Functions 5-1 Angles5-2 Trigonometric Functions5-3 Trigonometric Function Values and Angle Measures5-4 Solutions and Applications of Right TrianglesThe Circular Functions and Their Graphs 6-1 Radian Measure6-2 The Unit Circle and Circular Functions6-3 Graphs of the Sine and Cosine Functions6-4 Translations of the Graphs of the Sine and Cosine Functions6-5 Graphs of the Tangent and Cotangent Functions6-6 Graphs of the Secant and Cosecant Functions6-7 Harmonic MotionTrigonometric Identities and Equations 7-1 Fundamental Identities7-2 Verifying Trigonometric Identities7-3 Sum and Difference Identities7-4 Double-Angle and Half-Angle Identities7-5 Inverse Circular Functions7-6 Trigonometric Equations7-7 Equations Involving Inverse Trigonometric FunctionsApplications of Trigonometry 8-1 The Law of Sines8-2 The Law of Cosines8-3 Geometrically Defined Vectors and Applications8-4 Algebraically Defined Vectors and the Dot Product8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers8-7 Polar Equations and Graphs8-8 Parametric Equations, Graphs, and ApplicationsSystems and Matrices 9-1 Systems of Linear Equations9-2 Matrix Solution of Linear Systems9-3 Determinant Solution of Linear Systems9-4 Partial Fractions9-5 Nonlinear Systems of Equations9-6 Systems of Inequalities and Linear Programming9-7 Properties of Matrices9-8 Matrix InversesAnalytic Geometry 10-1 Parabolas10-2 Ellipses10-3 Hyperbolas10-4 Summary of the Conic SectionsFurther Topics in Algebra 11-1 Sequences and Series11-2 Arithmetic Sequences and Series11-3 Geometric Sequences and Series11-4 The Binomial Theorem11-5 Mathematical Induction11-6 Basics of Counting Theory11-7 Basics of ProbabilityAppendix A Polar Form of Conic Sections Appendix B Rotation of Axes Appendix C Geometry Formulas