Precalculus

About our authors Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

• F. Foundations: A Prelude to Functions F.1 The Distance and Midpoint FormulasF.2 Graphs of Equations in Two Variables; Intercepts; SymmetryF.3 LinesF.4 CirclesChapter Project Functions and Their Graphs 1.1 Functions1.2 The Graph of a Function1.3 Properties of Functions1.4 Library of Functions; Piecewise-defined Functions1.5 Graphing Techniques: Transformations1.6 Mathematical Models: Building Functions1.7 Building Mathematical Models Using VariationChapter ReviewChapter TestChapter Projects Linear and Quadratic Functions 2.1 Properties of Linear Functions and Linear Models2.2 Building Linear Models from Data2.3 Quadratic Functions and Their Zeros2.4 Properties of Quadratic Functions2.5 Inequalities Involving Quadratic Functions2.6 Building Quadratic Models from Verbal Descriptions and from Data2.7 Complex Zeros of a Quadratic Function2.8 Equations and Inequalities Involving the Absolute Value FunctionChapter ReviewChapter TestCumulative ReviewChapter Projects Polynomial and Rational Functions 3.1 Polynomial Functions and Models3.2 The Real Zeros of a Polynomial Function3.3 Complex Zeros; Fundamental Theorem of Algebra3.4 Properties of Rational Functions3.5 The Graph of a Rational Function3.6 Polynomial and Rational InequalitiesChapter ReviewChapter TestCumulative ReviewChapter Projects Exponential and Logarithmic Functions 4.1 Composite Functions4.2 One-to-One Functions; Inverse Functions4.3 Exponential Functions4.4 Logarithmic Functions4.5 Properties of Logarithms4.6 Logarithmic and Exponential Equations4.7 Financial Models4.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models4.9 Building Exponential, Logarithmic, and Logistic Models from DataChapter ReviewChapter TestCumulative ReviewChapter Projects Trigonometric Functions 5.1 Angles and Their Measure5.2 Trigonometric Functions: Unit Circle Approach5.3 Properties of the Trigonometric Functions5.4 Graphs of the Sine and Cosine Functions5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions5.6 Phase Shift; Sinusoidal Curve FittingChapter ReviewChapter TestCumulative ReviewChapter Projects Analytic Trigonometry 6.1 The Inverse Sine, Cosine, and Tangent Functions6.2 The Inverse Trigonometric Functions (Continued)6.3 Trigonometric Equations6.4 Trigonometric Identities6.5 Sum and Difference Formulas6.6 Double-angle and Half-angle Formulas6.7 Product-to-Sum and Sum-to-Product FormulasChapter ReviewChapter TestCumulative ReviewChapter Projects Applications of Trigonometric Functions 7.1 Right Triangle Trigonometry; Applications7.2 The Law of Sines7.3 The Law of Cosines7.4 Area of a Triangle7.5 Simple Harmonic Motion; Damped Motion; Combining WavesChapter ReviewChapter TestCumulative ReviewChapter Projects Polar Coordinates; Vectors 8.1 Polar Coordinates8.2 Polar Equations and Graphs8.3 The Complex Plane; De Moivre’s Theorem8.4 Vectors8.5 The Dot Product8.6 Vectors in Space8.7 The Cross ProductChapter ReviewChapter TestCumulative ReviewChapter Projects Analytic Geometry 9.1 Conics9.2 The Parabola9.3 The Ellipse9.4 The Hyperbola9.5 Rotation of Axes; General Form of a Conic9.6 Polar Equations of Conics9.7 Plane Curves and Parametric EquationsChapter ReviewChapter TestCumulative ReviewChapter Projects Systems of Equations and Inequalities 10.1 Systems of Linear Equations: Substitution and Elimination10.2 Systems of Linear Equations: Matrices10.3 Systems of Linear Equations: Determinants10.4 Matrix Algebra10.5 Partial Fraction Decomposition10.6 Systems of Nonlinear Equations10.7 Systems of Inequalities10.8 Linear ProgrammingChapter ReviewChapter TestCumulative ReviewChapter Projects Sequences; Induction; the Binomial Theorem 11.1 Sequences11.2 Arithmetic Sequences11.3 Geometric Sequences; Geometric Series11.4 Mathematical Induction11.5 The Binomial TheoremChapter ReviewChapter TestCumulative ReviewChapter Projects Counting and Probability 12.1 Counting12.2 Permutations and Combinations12.3 ProbabilityChapter ReviewChapter TestCumulative ReviewChapter Projects A Preview of Calculus: The Limit, Derivative, and Integral of a Function 13.1 Finding Limits Using Tables and Graphs13.2 Algebra Techniques for Finding Limits13.3 One-sided Limits; Continuous Functions13.4 The Tangent Problem; The Derivative13.5 The Area Problem; The IntegralChapter ReviewChapter TestChapter Projects Appendix A: Review A.1 Algebra EssentialsA.2 Geometry EssentialsA.3 PolynomialsA.4 Factoring PolynomialsA.5 Synthetic DivisionA.6 Rational ExpressionsA.7 nth Roots; Rational ExponentsA.8 Solving EquationsA.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job ApplicationsA.10 Interval Notation; Solving InequalitiesA.11 Complex NumbersAppendix B: Graphing Utilities B.1 The Viewing RectangleB.2 Using a Graphing Utility to Graph EquationsB.3 Using a Graphing Utility to Locate Intercepts and Check for SymmetryB.4 Using a Graphing Utility to Solve EquationsB.5 Square ScreensB.6 Using a Graphing Utility to Graph InequalitiesB.7 Using a Graphing Utility to Solve Systems of Linear EquationsB.8 Using a Graphing Utility to Graph a Polar EquationB.9 Using a Graphing Utility to Graph Parametric Equations AnswersPhoto CreditsIndex