Contents
Preface
Instructor Resources
Student Resources
Acknowledgments
Ch 1: Functions and Their Graphs
Introduction to Library of Parent Functions
Section 1.1: Lines in the Plane
Section 1.2: Functions
Section 1.3: Graphs of Functions
Section 1.4: Shifting, Reflecting, and Stretching Graphs
Section 1.5: Combinations of Functions
Section 1.6: Inverse Functions
Section 1.7: Linear Models and Scatter Plots
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Ch 2: Polynomial and Rational Functions
Section 2.1: Quadratic Functions
Section 2.2: Polynomial Functions of Higher Degree
Section 2.3: Real Zeros of Polynomial Functions
Section 2.4: Complex Numbers
Section 2.5: The Fundamental Theorem of Algebra
Section 2.6: Rational Functions and Asymptotes
Section 2.7: Graphs of Rational Functions
Section 2.8: Quadratic Models
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Progressive Summary (Chapters 1-2)
Ch 3: Exponential and Logarithmic Functions
Section 3.1: Exponential Functions and Their Graphs
Section 3.2: Logarithmic Functions and Their Graphs
Section 3.3: Properties of Logarithms
Section 3.4: Solving Exponential and Logarithmic Equations
Section 3.5: Exponential and Logarithmic Models
Section 3.6: Nonlinear Models
Chapter Summary
Review Exercises
Chapter Test
Cumulative Test: Chapters 1-3
Proofs in Mathematics
Progressive Summary (Chapters 1-3)
Ch 4: Trigonometric Functions
Section 4.1: Radian and Degree Measure
Section 4.2: Trigonometric Functions: The Unit Circle
Section 4.3: Right Triangle Trigonometry
Section 4.4: Trigonometric Functions of Any Angle
Section 4.5: Graphs of Sine and Cosine Functions
Section 4.6: Graphs of Other Trigonometric Functions
Section 4.7: Inverse Trigonometric Functions
Section 4.8: Applications and Models
Chapter Summary
Review Exercises
Chapter Test
Library of Parent Functions Review
Proofs in Mathematics
Ch 5: Analytic Trigonometry
Section 5.1: Using Fundamental Identities
Section 5.2: Verifying Trigonometric Identities
Section 5.3: Solving Trigonometric Equations
Section 5.4: Sum and Difference Formulas
Section 5.5: Multiple-Angle and Product-to-Sum Formulas
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Ch 6: Additional Topics in Trigonometry
Section 6.1: Law of Sines
Section 6.2: Law of Cosines
Section 6.3: Vectors in the Plane
Section 6.4: Vectors and Dot Products
Section 6.5: Trigonometric Form of a Complex Number
Chapter Summary
Review Exercises
Chapter Test
Cumulative Test: Chapters 4-6
Proofs in Mathematics
Progressive Summary (Chapters 1-6)
Ch 7: Linear Systems and Matrices
Section 7.1: Solving Systems of Equations
Section 7.2: Systems of Linear Equations in Two Variables
Section 7.3: Multivariable Linear Systems
Section 7.4: Matrices and Systems of Equations
Section 7.5: Operations with Matrices
Section 7.6: The Inverse of a Square Matrix
Section 7.7: The Determinant of a Square Matrix
Section 7.8: Applications of Matrices and Determinants
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Ch 8: Sequences, Series, and Probability
Section 8.1: Sequences and Series
Section 8.2: Arithmetic Sequences and Partial Sums
Section 8.3: Geometric Sequences and Series
Section 8.4: The Binomial Theorem
Section 8.5: Counting Principles
Section 8.6: Probability
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Ch 9: Topics in Analytic Geometry
Section 9.1: Circles and Parabolas
Section 9.2: Ellipses
Section 9.3: Hyperbolas and Rotation of Conics
Section 9.4: Parametric Equations
Section 9.5: Polar Coordinates
Section 9.6: Graphs of Polar Equations
Section 9.7: Polar Equations of Conics
Chapter Summary
Review Exercises
Chapter Test
Cumulative Test: Chapters 7-9
Proofs in Mathematics
Progressive Summary (Chapters 3-9)
Ch 10: Analytic Geometry in Three Dimensions
Section 10.1: The Three-Dimensional Coordinate System
Section 10.2: Vectors in Space
Section 10.3: The Cross Product of Two Vectors
Section 10.4: Lines and Planes in Space
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
Appendices
Appendix A: Technology Support Guide
Answers to Odd-Numbered Exercises and Tests
Index of Selected Applications
Index