Table of Contents

Chapter 1 • Functions and Their Graphs
 Slope of a Line through Two Points
 Equation of a Straight Line: Standard and Point–Slope Forms
 Equation of a Straight Line: Slope–Intercept Form
 Linear Functions in Different Forms
 Slopes and Intercepts of Linear Functions
 Equations of Parallel and Perpendicular Lines
 Relations and Functions
 Polynomial Functions
 Domain and Range of a Piecewise Function
 Domain and Range of a Function
 Increasing and Decreasing Intervals of a Function
 Graphs of Piecewise Functions
 Even and Odd Functions
 Function Transformations: Dilation
 Combining Functions
 Composite Functions
 Inverse of a Function

Chapter 2 • Polynomial and Rational Functions
 Graphing Quadratic Functions
 Graphing Cubic Functions
 Zeros of Polynomial Functions
 Forming a Quadratic Equation from its Roots
 Intermediate Value Theorem
 Polynomial Long Division without Remainder
 Remainder and Factor Theorem with Synthetic Division
 Rational Zeros Theorem
 Equating, Adding, and Subtracting Complex Numbers
 Multiplying Complex Numbers
 Solving Quadratic Equations with Complex Roots
 Real and Complex Roots of Polynomials
 Linear Factorization and Conjugate Root Theorems
 Domain and Range of a Rational Function
 Graphs of Rational Functions
 Scatter Plots and Lines of Best Fit

Chapter 3 • Exponential and Logarithmic Functions
 Monomial Functions
 Graphs of Exponential Functions
 Compound Interest
 Graphs of Logarithmic Functions
 Laws of Logarithms
 Simplifying Natural Logarithmic Expressions
 Solving Exponential Equations Using Exponent Properties
 Solving Exponential Equations Using Logarithms
 Natural Exponential Equations
 Logarithmic Equations with Like Bases
 Natural Logarithmic Equations
 Exponential Growth and Decay Models
 The Logistic Model

Chapter 4 • Trigonometric Functions
 Angles in Standard Position
 Conversion between Radians and Degrees
 Arc Lengths and Sectors
 Trigonometric Ratios on the Unit Circle
 Evaluating Trigonometric Functions with a Calculator
 Trigonometric Ratios in Right Triangles
 Evaluating Trigonometric Function Values with Angles 30, 45, and 60
 Trigonometric Functions Values with Reference Angles
 Graphs of Trigonometric Functions
 Transformation of Trigonometric Functions
 The Graphs of Reciprocal Trigonometric Functions
 Inverse Trigonometric Functions
 The Cosine Ratio
 Angles of Elevation and Depression
 Chapter 5 • Analytic Trigonometry
 Chapter 6 • Additional Topics in Trigonometry

Chapter 7 • Linear Systems and Matrices
 Solving Systems of Linear Equations Using Substitution
 Solving Systems of Linear Equations Graphically
 Solving Systems of Linear Equations Using Elimination
 Systems of Linear Equations in Three Variables
 Rank of a Matrix
 Equal Matrices
 Adding and Subtracting Matrices
 Scalar Multiplication of Matrices
 Matrix Multiplication
 Properties of Matrix Multiplication
 Inverse of a 2 × 2 Matrix
 Inverse of a Matrix: The Adjoint Method
 ThreebyThree Determinants
 TwobyTwo Determinants
 Cramer’s Rule

Chapter 8 • Sequences, Series, and Probability
 Recursive Formula of a Sequence
 Sigma Notation
 Calculations with Arithmetic Sequences
 Using Arithmetic Sequence Formulas
 Geometric Sequences
 Finding the nth Term of a Geometric Sequence
 Sum of a Finite Geometric Sequence
 Sum of an Infinite Geometric Sequence
 The Binomial Theorem
 Pascal’s Triangle and the Binomial Theorem
 Properties of Permutations
 Properties of Combinations
 Introduction to Probability
 Probability of Simple Events
 Compound Events

Chapter 9 • Topics in Analytic Geometry
 Equation of a Circle
 Equation of a Circle Passing through Three Noncollinear Points
 Equation of an Ellipse
 Equation of a Hyperbola
 Conversion between Parametric and Rectangular Equations
 Polar Coordinates
 Conversion between Rectangular and Polar Equations
 Graphing Polar Curves
 Polar Equation of a Conic
 Chapter 10 • Analytic Geometry in Three Dimensions
 Chapter 11 • Limits and an Introduction to Calculus
 Appendix A • Technology Support Guide
 Appendix B • Concepts in Statistics
 Appendix C • Review of Graphs, Equations, and Inequalities
 Appendix D • Variation
 Appendix E • Solving Linear Equations and Inequalities
 Appendix F • Systems of Inequalities
 Appendix G • Mathematical Induction