Precalculus with Limits: A Graphing Approach

Note: Each chaper concludes with a Chapter Summary, Review Exercises, and a Chapter Test. 1. Functions and Their Graphs Introduction to Library of Functions 1.1 Lines in the Plane 1.2 Functions 1.3 Graphs of Functions 1.4 Shifting, Reflecting, and Stretching Graphs 1.5 Combinations of Functions 1.6 Inverse Functions 1.7 Exploring Data: Linear Models and Scatter Plots 2. Polynomial and Rational Functions 2.1 Quadratic Functions 2.2 Polynomial Functions of Higher Degree 2.3 Real Zeros of Polynomial Functions 2.4 Complex Numbers 2.5 The Fundamental Theorem of Algebra 2.6 Rational Functions and Asymptotes 2.7 Graphs of Rational Functions 2.8 Exploring Data: Quadratic Models 3. Exponential and Logarithmic Functions 3.1 Exponential Functions and Their Graphs 3.2 Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Exponential and Logarithmic Equations 3.5 Exponential and Logarithmic Models 3.6 Exploring Data: Nonlinear Models Cumulative Test: Chapters 1-3 4. Trigonometric Functions 4.1 Radian and Degree Measure 4.2 Trigonmetric Functions: The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric Functions of Any Angle 4.5 Graphs of Sine and Cosine Functions 4.6 Graphs of Other Trigonometric Functions 4.7 Inverse Trigonometric Functions 4.8 Applications and Models 5. Analytic Trigonometry 5.1 Using Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Solving Trigonometric Equations 5.4 Sum and Difference Formulas 5.5 Multiple-Angle and Product-to-Sum Formulas 6. Additional Topics in Trigonometry 6.1 Law of Sines 6.2 Law of Cosines 6.3 Vectors in the Plane 6.4 Vectors and Dot Products 6.5 Trigonometric Form of a Complex Number Cumulative Test: Chapters 4-6 7. Linear Systems and Matrices 7.1 Solving Systems of Equations 7.2 Systems of Linear Equations in Two Variables 7.3 Multivariable Linear Systems 7.4 Matrices and Systems of Equations 7.5 Operations with Matrices 7.6 The Inverse of a Square Matrix 7.7 The Determinant of a Square Matrix 7.8 Applications of Matrices and Determinants 8. Sequences, Series, and Probability 8.1 Sequences and Series 8.2 Arithmetic Sequences and Partial Sums 8.3 Geometric Sequences and Series 8.4 Mathematical Induction 8.5 The Binomial Theorem 8.6 Counting Principles 8.7 Probability 9. Topics in Analytic Geometry 9.1 Introduction to Conics: Parabolas 9.2 Ellipses 9.3 Hyperbolas 9.4 Rotation and Systems of Quadratic Equations 9.5 Parametric Equations 9.6 Polar Coordinates 9.7 Graphs of Polar Equations 9.8 Polar Equations of Conics Cumulative Test: Chapters 7-9 10. Analytic Geometry in Three Dimensions 10.1 The Three-Dimensional Coordinate System 10.2 Vectors in Space 10.3 The Cross Product of Two Vectors 10.4 Lines and Planes in Space 11. Limits and an Introduction to Calculus 11.1 Introduction to Limits 11.2 Techniques for Evaluating Limits 11.3 The Tangent Line Problem 11.4 Limits at Infinity and Limits of Sequences 11.5 The Area Problem Cumulative Test: Chapters 10-11 Appendix A Technology Support Guide Appendix B Review of Graphs, Equations, and Inequalities B.1 The Cartesian Plane B.2 Graphs of Equations B.3 Solving Equations Algebraically and Graphically B.4 Solving Inequalities Algebraically and Graphically B.5 Exploring Data: Representing Data Graphically Appendix C Proofs of Selected Theorems Appendix D Concepts in Statistics D.1 Measures of Central Tendency and Dispersion D.2 Least Squares Regression Appendix E Solving Linear Equations and Inequalities Appendix F Systems of Inequalities F.1 Solving Systems of Inequalities F.2 Linear Programming