Precalculus

PrefaceAcknowledgmentsTo the StudentChapter 1 The Foundations of Algebra 1.1 The Real Number System 1.2 Polynomials and Factoring 1.3 Exponents, Radicals, and Complex Numbers 1.4 Linear Equations and Linear Inequalities in One Unknown 1.5 Absolute Value in Equations and Inequalities 1.6 Second-Degree InequalitiesChapter 2 Functions and Graphs 2.1 The Rectangular Coordinate System 2.2 Functions and Function Notation 2.3 Graphs of Functions 2.4 Aids in Graphing 2.5 Linear Functions 2.6 Quadratic Equations 2.7 Quadratic Functions 2.8 Combining Functions; Inverse FunctionsChapter 3 Roots of Polynomials 3.1 Synthetic Division; The Remainder and Factor Theorems 3.2 Graphs of Polynomial Functions 3.3 The Rational Root Theorem and the Depressed Equation 3.4 Rational Functions and Their Graphs 3.5 Partial FractionsChapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Fundamental Properties of Logarithms 4.4 Computing with Logarithms (Optional) 4.5 Exponential and Logarithmic EquationsChapter 5 Trigonometry: The Circular Functions 5.0 Review of Geometry 5.1 The Wrapping Function 5.2 The Sine, Cosine, and Tangent Functions 5.3 Graphs of Sine, Cosine, and Tangent 5.4 Values of Sine, Cosine, and Tangent 5.5 Graphs: Amplitude, Period, and Phase Shift 5.6 Secant, Cosecant, and Cotangent 5.7 The Inverse Trigonometric FunctionsChapter 6 Angles and Triangles 6.1 Angles and Their Measurement 6.2 Trigonometric Functions of Angles 6.3 Right Triangle Trigonometry 6.4 Law of Cosines 6.5 Law of SinesChapter 7 Analytic Trigonometry 7.1 Trigonometric Identities 7.2 The Addition Formulas 7.3 Double- and Half-Angle Formulas 7.4 The Product-Sum Formulas 7.5 Trigonometric EquationsChapter 8 Complex Numbers and the Fundamental Theorem of Algebra 8.1 Complex Numbers and Their Properties 8.2 Trigonometry and Complex Numbers 8.3 The Fundamental Theorem of Algebra 8.4 Descartes's Rule of SignsChapter 9 Analytic Geometry: The Conic Sections 9.1 Analytic Geometry 9.2 The Circle 9.3 The Parabola 9.4 The Ellipse 9.5 The Hyperbola 9.6 Translation of Axes 9.7 Rotation of Axes 9.8 Polar Coordinates 9.9 Parametric EquationsChapter 10 Systems of Equations and Inequalities 10.1 Systems of Equations 10.2 Systems of Linear Inequalities 10.3 Linear Programming (Optional) 10.4 Systems of Linear Equations in Three Unknowns 10.5 Matrices and Linear Systems 10.6 Matrix Operations and Applications (Optional) 10.7 Inverses of Matrices (Optional) 10.8 Determinants and Cramer's RuleChapter 11 Sequences and Series 11.1 Sequences and Sigma Notation 11.2 Arithmetic Sequences 11.3 Geometric Sequences 11.4 Mathematical Induction 11.5 The Binomial TheoremAppendix A. ApplicationsAppendix B. Limits: A Preview of CalculusTables AppendixAnswers to Odd-Numbered Exercises and to Review Exercises and Progress TestsSolutions to Selected Review ExercisesIndex