Table of Contents

1 Functions

1.1 Functions and Function Notation
 Recognizing Functions from Graphs
 Representing Relations
 Determining Whether a Relation Is a Function
 Recognizing Functions from Diagrams and Sets
 Completing Function Tables and Finding Function Rules
 Completing Function Tables
 Evaluating a Function at a Given Value
 Writing an Equation to Represent a Function
 Finding the Value of Functions from Graphs
 1.2 Domain and Range
 1.3 Rates of Change and Behavior of Graphs
 1.4 Composition of Functions
 1.5 Transformation of Functions
 1.6 Absolute Value Functions
 1.7 Inverse Functions

1.1 Functions and Function Notation

2 Linear Functions

2.1 Linear Functions
 Slope of a Line from Tables and Graphs
 Slope from Two Points
 Determining the Slope of a Line from a Graph, a Table, or Coordinates
 Finding Coordinates given the Slope
 Equation of a Line through Two Points
 Linear Equations with Variables on Both Sides
 Equation of a Straight Line in Different Forms
 Linear Equations in Standard Form
 Applications of Linear Equations
 Linear Equations in PointSlope Form
 2.2 Graphs of Linear Functions
 2.3 Modeling with Linear Functions
 2.4 Fitting Linear Models to Data

2.1 Linear Functions

3 Polynomial and Rational Functions

3.1 Complex Numbers
 Operations with Complex Numbers in Polar Form
 Exponential Form of a Complex Number
 Introduction to Complex Numbers
 Purely Imaginary Numbers
 Argand Diagrams
 Addition and Subtraction of Complex Numbers
 Multiplication of Complex Numbers
 Complex Conjugates
 Modulus of a Complex Number
 Argument of a Complex Number
 3.2 Quadratic Functions
 3.3 Power Functions and Polynomial Functions
 3.4 Graphs of Polynomial Functions
 3.5 Dividing Polynomials
 3.6 Zeros of Polynomial Functions
 3.7 Rational Functions
 3.8 Inverses and Radical Functions
 3.9 Modeling Using Variation

3.1 Complex Numbers

4 Exponential and Logarithmic Functions
 4.1 Exponential Functions
 4.2 Graphs of Exponential Functions

4.3 Logarithmic Functions
 Converting Exponential Expressions to Logarithmic Form
 Converting Logarithmic Expressions to Exponential Form
 Writing a Logarithmic Equation in Exponential Form
 Converting Equations between Logarithmic and Exponential Forms
 Logarithmic Equations
 Logarithmic Equations with Different Bases
 Natural Logarithmic Equations
 4.4 Graphs of Logarithmic Functions
 4.5 Logarithmic Properties
 4.6 Exponential and Logarithmic Equations
 4.7 Exponential and Logarithmic Models
 4.8 Fitting Exponential Models to Data

5 Trigonometric Functions
 5.1 Angles
 5.2 Unit Circle: Sine and Cosine Functions
 5.3 The Other Trigonometric Functions

5.4 Right Triangle Trigonometry

6 Periodic Functions
 6.1 Graphs of the Sine and Cosine Functions
 6.2 Graphs of the Other Trigonometric Functions
 6.3 Inverse Trigonometric Functions

7 Trigonometric Identities and Equations

7.1 Solving Trigonometric Equations with Identities
 7.2 Sum and Difference Identities
 7.3 DoubleAngle, HalfAngle, and Reduction Formulas
 7.4 SumtoProduct and ProducttoSum Formulas
 7.5 Solving Trigonometric Equations
 7.6 Modeling with Trigonometric Equations

7.1 Solving Trigonometric Equations with Identities

8 Further Applications of Trigonometry
 8.1 NonRight Triangles: Law of Sines
 8.2 NonRight Triangles: Law of Cosines
 8.3 Polar Coordinates
 8.4 Polar Coordinates: Graphs
 8.5 Polar Form of Complex Numbers
 8.6 Parametric Equations
 8.7 Parametric Equations: Graphs
 8.8 Vectors

9 Systems of Equations and Inequalities
 9.1 Systems of Linear Equations: Two Variables
 9.2 Systems of Linear Equations: Three Variables
 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
 9.4 Partial Fractions
 9.5 Matrices and Matrix Operations
 9.6 Solving Systems with Gaussian Elimination
 9.7 Solving Systems with Inverses
 9.8 Solving Systems with Cramer’s Rule

10 Analytic Geometry
 10.1 The Ellipse
 10.2 The Hyperbola
 10.3 The Parabola
 10.4 Rotation of Axis
 10.5 Conic Sections in Polar Coordinates

11 Sequences, Probability and Counting Theory
 11.1 Sequences and Their Notations
 11.2 Arithmetic Sequences
 11.3 Geometric Sequences
 11.4 Series and Their Notations
 11.5 Counting Principles
 11.6 Binomial Theorem
 11.7 Probability

12 Introduction to Calculus
 12.1 Finding Limits: Numerical and Graphical Approaches
 12.2 Finding Limits: Properties of Limits
 12.3 Continuity
 12.4 Derivatives