Table of Contents

1 Graphs
 1.1 The Distance and Midpoint Formulas
 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
 1.3 Lines
 1.4 Circles

2 Functions and Their Graphs
 2.1 Functions
 2.2 The Graph of a Function
 2.3 Properties of Functions
 2.4 Library of Functions: PiecewiseDefined Functions
 2.5 Graphing Techniques: Transformations
 2.6 Mathematical Models: Building Functions

3 Linear and Quadratic Functions
 3.1 Properties of Linear Functions and Linear Models
 3.2 Building Linear Models from Data
 3.3 Quadratic Functions and Their Properties
 3.4 Build Quadratic Models from Verbal Descriptions and from Data
 3.5 Inequalities Involving Quadratic Functions

4 Polynomial and Rational Functions
 4.1 Polynomial Functions and Models
 4.2 Properties of Rational Functions
 4.3 The Graph of a Rational Function
 4.4 Polynomial and Rational Inequalities
 4.5 The Real Zeros of a Polynomial Function
 4.6 Complex Zeros: Fundamental Theorem of Algebra

5 Exponential and Logarithmic Functions
 5.1 Composite Functions
 5.2 OnetoOne Functions; Inverse Functions
 5.3 Exponential Functions
 5.4 Logarithmic Functions
 5.5 Properties of Logarithms
 5.6 Logarithmic and Exponential Equations
 5.7 Financial Models

5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
 5.9 Building Exponential, Logarithmic, and Logistic Models from Data

6 Trigonometric Functions
 6.1 Angles and Their Measure
 6.2 Trigonometric Functions: Unit Circle Approach
 6.3 Properties of the Trigonometric Functions
 6.4 Graphs of the Sine and Cosine Functions
 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
 6.6 Phase Shift; Sinusoidal Curve Fitting

7 Analytic Trigonometry
 7.1 The Inverse Sine, Cosine, and Tangent Functions
 7.2 The Inverse Trigonometric Functions (Continued)
 7.3 Trigonometric Equations

7.4 Trigonometric Identities
 7.5 Sum and Difference Formulas
 7.6 DoubleAngle and HalfAngle Formulas
 7.7 ProducttoSum and SumtoProduct Formulas

8 Applications of Trigonometric Functions
 8.1 Right Triangle Trigonometry; Applications
 8.2 The Law of Sines
 8.3 The Law of Cosines
 8.4 Area of a Triangle

8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

9 Polar Coordinates; Vectors
 9.1 Polar Coordinates
 9.2 Polar Equations and Graphs
 9.3 The Complex Plane; De Moivre’s Theorem
 9.4 Vectors
 9.5 The Dot Product
 9.6 Vectors in Space
 9.7 The Cross Product

10 Analytic Geometry
 10.1 Conics
 10.2 The Parabola
 10.3 The Ellipse
 10.4 The Hyperbola
 10.5 Rotation of Axes; General Form of a Conic
 10.6 Polar Equations of Conics
 10.7 Plane Curves and Parametric Equations

11 Systems of Equations and Inequalities

11.1 Systems of Linear Equations: Substitution and Elimination
 Systems of Equations with Substitution
 Solving Systems of Linear Equations by Elimination
 Number of Solutions to a System of Linear Equations
 Using Systems of Equations to Investigate Profits
 Applications of Systems of Equations
 Applications of Systems of Equations in Three Variables
 Inconsistent Systems of Equations in Three Variables
 Systems of Linear Equations in Three Variables
 11.2 Systems of Linear Equations: Matrices
 11.3 Systems of Linear Equations: Determinants
 11.4 Matrix Algebra
 11.5 Partial Fraction Decomposition
 11.6 Systems of Nonlinear Equations
 11.7 Systems of Inequalities
 11.8 Linear Programming

11.1 Systems of Linear Equations: Substitution and Elimination

12 Sequences; Induction; the Binomial Theorem
 12.1 Sequences
 12.2 Arithmetic Sequences
 12.3 Geometric Sequences; Geometric Series
 12.4 Mathematical Induction
 12.5 The Binomial Theorem

13 Counting and Probability
 13.1 Counting
 13.2 Permutations and Combinations
 13.3 Probability

14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
 14.1 Finding Limits Using Tables and Graphs
 14.2 Algebra Techniques for Finding Limits
 14.3 OneSided Limits; Continuous Functions
 14.4 The Tangent Problem; The Derivative

14.5 The Area Problem; The Integral