Precalculus

Description

Cover Title Page Copyright Page Contents Preface Acknowledgments To the Student About the Author Applications Index A B C D E F G H I J K L M N O P R S T V W X Y P: Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials P.5 Factoring Polynomials Mid-Chapter Check Point P.6 Rational Expressions P.7 Equations P.8 Modeling with Equations P.9 Linear Inequalities and Absolute Value Inequalities Summary, Review, and Test Review Exercises Chapter P: Test 1 Functions and Graphs 1.1 Graphs and Graphing Utilities 1.2 Basics of Functions and Their Graphs 1.3 More on Functions and Their Graphs 1.4 Linear Functions and Slope 1.5 More on Slope Mid-Chapter Check Point 1.6 Transformations of Functions 1.7 Combinations of Functions; Composite Functions 1.8 Inverse Functions 1.9 Distance and Midpoint Formulas; Circles 1.10 Modeling with Functions Summary, Review, and Test Review Exercises Chapter 1 Test 2 Polynomial and Rational Functions 2.1 Complex Numbers 2.2 Quadratic Functions 2.3 Polynomial Functions and Their Graphs 2.4 Dividing Polynomials; Remainder and Factor Theorems 2.5 Zeros of Polynomial Functions Mid-Chapter Check Point 2.6 Rational Functions and Their Graphs 2.7 Polynomial and Rational Inequalities 2.8 Modeling Using Variation Summary, Review, and Test Review Exercises Chapter 2 Test Cumulative Review Exercises (Chapters P–2) 3 Exponential and Logarithmic Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Properties of Logarithms Mid-Chapter Check Point 3.4 Exponential and Logarithmic Equations 3.5 Exponential Growth and Decay; Modeling Data Summary, Review, and Test Review Exercises Chapter 3 Test Cumulative Review Exercises (Chapters P–3) 4 Trigonometric Functions 4.1 Angles and Radian Measure 4.2 Trigonometric Functions: The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric Functions of Any Angle Mid-Chapter Check Point 4.5 Graphs of Sine and Cosine Functions 4.6 Graphs of Other Trigonometric Functions 4.7 Inverse Trigonometric Functions 4.8 Applications of Trigonometric Functions Summary, Review, and Test Review Exercises Chapter 4 Test Cumulative Review Exercises (Chapters P–4) 5 Analytic Trigonometry 5.1 Verifying Trigonometric Identities 5.2 Sum and Difference Formulas 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas Mid-Chapter Check Point 5.4 Product-to-Sum and Sum-to-Product Formulas 5.5 Trigonometric Equations Summary, Review, and Test Review Exercises Chapter 5 Test Cumulative Review Exercises (Chapters P–5) 6 Additional Topics in Trigonometry 6.1 The Law of Sines 6.2 The Law of Cosines 6.3 Polar Coordinates 6.4 Graphs of Polar Equations Mid-Chapter Check Point 6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem 6.6 Vectors 6.7 The Dot Product Summary, Review, and Test Review Exercises Chapter 6 Test Cumulative Review Exercises (Chapters P–6) 7 Systems of Equations and Inequalities 7.1 Systems of Linear Equations in Two Variables 7.2 Systems of Linear Equations in Three Variables 7.3 Partial Fractions 7.4 Systems of Nonlinear Equations in Two Variables Mid-Chapter Check Point 7.5 Systems of Inequalities 7.6 Linear Programming Summary, Review, and Test Review Exercises Chapter 7 Test Cumulative Review Exercises (Chapters P–7) 8 Matrices and Determinants 8.1 Matrix Solutions to Linear Systems 8.2 Inconsistent and Dependent Systems and Their Applications 8.3 Matrix Operations and Their Applications Mid-Chapter Check Point 8.4 Multiplicative Inverses of Matrices and Matrix Equations 8.5 Determinants and Cramer’s Rule Summary, Review, and Test Review Exercises Chapter 8 Test Cumulative Review Exercises (Chapters P–8) 9 Conic Sections and Analytic Geometry 9.1 The Ellipse 9.2 The Hyperbola 9.3 The Parabola Mid-Chapter Check Point 9.4 Rotation of Axes 9.5 Parametric Equations 9.6 Conic Sections in Polar Coordinates Summary, Review, and Test Review Exercises Chapter 9 Test Cumulative Review Exercises (Chapters P–9) 10 Sequences, Induction, and Probability 10.1 Sequences and Summation Notation 10.2 Arithmetic Sequences 10.3 Geometric Sequences and Series Mid-Chapter Check Point 10.4 Mathematical Induction 10.5 The Binomial Theorem 10.6 Counting Principles, Permutations, and Combinations 10.7 Probability Summary, Review, and Test Review Exercises Chapter 10 Test Cumulative Review Exercises (Chapters P–10) 11 Introduction to Calculus 11.1 Finding Limits Using Tables and Graphs 11.2 Finding Limits Using Properties of Limits 11.3 Limits and Continuity Mid-Chapter Check Point 11.4 Introduction to Derivatives Summary, Review, and Test Review Exercises Chapter 11 Test Cumulative Review Exercises (Chapters P–11) Appendix A: Where Did That Come From? Selected Proofs Appendix B: The Transition from Precalculus to Calculus Answers to Selected Exercises Subject Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Credit