## Table of Contents

**1. Graphs, Functions, and Models**

1.1 Introduction to Graphing

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

1.4 Equations of Lines and Modeling

1.5 Linear Equations, Functions, Zeros, and Applications

1.6 Solving Linear Inequalities

**2. More on Functions**

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

2.4 Symmetry

2.5 Transformations

2.6 Variation and Applications

**3. Quadratic Functions and Equations; Inequalities**

3.1 The Complex Numbers

3.2 Quadratic Equations, Functions, Zeros, and Models

3.3 Analyzing Graphs of Quadratic Functions

3.4 Solving Rational Equations and Radical Equations

3.5 Solving Equations and Inequalities with Absolute Value

**4. Polynomial Functions and Rational Functions**

4.1 Polynomial Functions and Models

4.2 Graphing Polynomial Functions

4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

4.6 Polynomial Inequalities and Rational Inequalities

**5. Exponential Functions and Logarithmic Functions**

5.1 Inverse Functions

5.2 Exponential Functions and Graphs

5.3 Logarithmic Functions and Graphs

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential Equations and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; Compound Interest

**6. The Trigonometric Functions**

6.1 Trigonometric Functions of Acute Angles

6.2 Applications of Right Triangles

6.3 Trigonometric Functions of Any Angle

6.4 Radians, Arc Length, and Angular Speed

6.5 Circular Functions: Graphs and Properties

6.6 Graphs of Transformed Sine and Cosine Functions

**7. Trigonometric Identities, Inverse Functions, and Equations**

7.1 Identities: Pythagorean and Sum and Difference

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

7.3 Proving Trigonometric Identities

7.4 Inverses of the Trigonometric Functions

7.5 Solving Trigonometric Equations

**8. Applications of Trigonometry**

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Complex Numbers: Trigonometric Notation

8.4 Polar Coordinates and Graphs

8.5 Vectors and Applications

8.6 Vector Operations

**9. Systems of Equations and Matrices**

9.1 Systems of Equations in Two Variables

9.2 Systems of Equations in Three Variables

9.3 Matrices and Systems of Equations

9.4 Matrix Operations

9.5 Inverses of Matrices

9.6 Determinants and Cramer’s Rule

9.7 Systems of Inequalities and Linear Programming

9.8 Partial Fractions

**10. Conic Sections**

10.1 The Parabola

10.2 The Circle and the Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Inequalities

10.5 Rotation of Axes

10.6 Polar Equations of Conics

10.7 Parametric Equations

**11. Sequences, Series, and Combinatorics**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 Combinatorics: Permutations

11.6 Combinatorics: Combinations

11.7 The Binomial Theorem

11.8 Probability