Table of Contents

1 Functions and Their Graphs
 1.1 Rectangular Coordinates
 1.2 Graphs of Equations
 1.3 Linear Equations in Two Variables
 1.4 Functions
 1.5 Analyzing Graphs of Functions
 1.6 A Library of Parent Functions
 1.7 Transformations of Functions
 1.8 Combinations of Functions: Composite Functions
 1.9 Inverse Functions
 1.10 Mathematical Modeling and Variation

2 Polynomial and Rational Functions
 2.1 Quadratic Functions and Models
 2.2 Polynomial Functions of Higher Degree
 2.3 Polynomial and Synthetic Division
 2.4 Complex Numbers
 2.5 Zeros of Polynomial Functions
 2.6 Rational Functions
 2.7 Nonlinear Inequalities

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 Exponential and Logarithmic Equations
 3.5 Exponential and Logarithmic Models

4 Trigonometry
 4.1 Radian and Degree Measure
 4.2 Trigonometric 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 MultipleAngle and ProducttoSum 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 The Complex Plane
 6.6 Trigonometric Form of a Complex Number

7 Systems of Equations and Inequalities
 7.1 Linear and Nonlinear Systems of Equations
 7.2 TwoVariable Linear Systems
 7.3 Multivariable Linear Systems
 7.4 Partial Fractions
 7.5 Systems of Inequalities
 7.6 Linear Programming

8 Matrices and Determinants
 8.1 Matrices and Systems of Equations
 8.2 Operations with Matrices
 8.3 The Inverse of a Square Matrix
 8.4 The Determinant of a Square Matrix
 8.5 Applications of Matrices and Determinants

9 Sequences, Series, and Probability
 9.1 Sequences and Series
 9.2 Arithmetic Sequences and Partial Sums
 9.3 Geometric Sequences and Series
 9.4 Mathematical Induction
 9.5 The Binomial Theorem
 9.6 Counting Principles
 9.7 Probability

10 Topics in Analytic Geometry
 10.1 Lines
 10.2 Introduction to Conics: Parabolas
 10.3 Ellipses
 10.4 Hyperbolas
 10.5 Rotation of Conics
 10.6 Parametric Equations
 10.7 Polar Coordinates
 10.8 Graphs of Polar Equations
 10.9 Polar Equations of Conics