Table of Contents

Properties of Functions and Graphs
 Symmetry of Graphs and Functions
 Absolute Value Functions
 Piecewise Functions
 Domain and Range of a Piecewise Function
 Graphs of Piecewise Functions
 Composite Functions
 Extrema of a Function Graph
 Function Transformations: Translations
 Function Transformations: Reflection
 Function Transformations: Dilation
 Inverse of a Function
 Graphs of Inverses of Functions
 Quadratic Functions

Polynomial Functions
 Simplifying Expressions: Rules of Exponents
 Monomial Functions
 Polynomial Functions
 Zeros of Polynomial Functions
 Real and Complex Roots of Polynomials
 Graphs of Polynomial Functions
 Polynomial Equations
 Dividing Polynomials by Monomials
 Dividing Polynomials by Binomials Using Factorization
 Polynomial Long Division without Remainder
 Polynomial Long Division with Remainder
 Synthetic Division
 Remainder and Factor Theorem with Synthetic Division
 Cubic Functions and Their Graphs
 Roots of Cubic Functions
 Descartes’ Rule of Signs
 Rational Zeros Theorem
 Linear Factorization and Conjugate Root Theorems

Rational and Radical Functions
 Adding and Subtracting Square Roots
 Multiplying and Dividing Square Roots
 Rationalizing Denominators
 Radical Equations
 Radical Functions
 Radical Inequalities
 Simplifying Algebraic Fractions
 Rational Equations
 Rational Functions
 Simplifying Rational Functions
 Domain and Range of a Rational Function
 Adding and Subtracting Rational Functions
 Multiplying and Dividing Rational Functions
 Horizontal and Vertical Asymptotes of a Function
 Graphs of Rational Functions
 Oblique Asymptotes
 Rational Inequalities

Exponential and Logarithmic Functions
 Solving Exponential Equations Using Exponent Properties
 Exponential Inequalities
 Evaluating Natural Exponential Expressions
 Natural Exponential Equations
 Logarithmic Functions
 Laws of Logarithms
 Evaluating Logarithms
 Converting between Logarithmic and Exponential Forms
 Graphs of Logarithmic Functions
 Simplifying Natural Logarithmic Expressions
 Natural Logarithmic Equations
 Solving Exponential Equations Using Logarithms
 Logarithmic Equations with Like Bases
 Logarithmic Equations with Different Bases
 Sequences and Series
 Sets

Probability and Statistics
 Geometric Probability
 Mutually Exclusive Events
 Independent Events
 Complementary Events
 Operations on Events
 Conditional Probability
 Conditional Probability: TwoWay Tables
 Dependent and Independent Events
 Compound Events
 Simulation Design
 Types of Statistical Studies
 Expected Values of Discrete Random Variables
 Standard Deviation of Discrete Random Variables
 Conic Sections

Matrices
 Introduction to Matrices
 Equal Matrices
 Scalar Multiplication of Matrices
 Adding and Subtracting Matrices
 Matrix Operations
 Matrix Multiplication
 Properties of Matrix Multiplication
 Power of a Matrix
 TwobyTwo Determinants
 ThreebyThree Determinants
 Cramer’s Rule
 Using Determinants to Calculate Areas
 Inverse of a 2 × 2 Matrix
 Solving a System of Two Equations Using a Matrix Inverse
 Inverse of a Matrix: The Adjoint Method
 Inverse of a Matrix: Row Operations
 Introduction to the System of Linear Equations
 Solving a System of Three Equations Using a Matrix Inverse
 Augmented Matrices
 Linear Transformation Definition
 Linear Transformations in Planes: Scaling
 Linear Transformations in Planes: Reflection
 Applications on Representing Data Using Matrices

Trigonometric Functions
 Angles in Standard Position
 Conversion between Radians and Degrees
 Arc Lengths
 Trigonometric Ratios on the Unit Circle
 Trigonometric Ratios in Right Triangles
 Signs of Trigonometric Functions in Quadrants
 Trigonometric Functions’ Values with Reference Angles
 Evaluating Trigonometric Functions with Special Angles
 Evaluating Trigonometric Ratios given the Value of Another Ratio
 Exact Values of Trigonometric Ratios
 Graphs of Trigonometric Functions
 Amplitude and Period of Trigonometric Functions
 Inverse Trigonometric Functions
 The Graphs of Reciprocal Trigonometric Functions
 Graphing Periodic Functions
 Transformation of Trigonometric Functions

Trigonometric Equations and Identities
 Simplifying Trigonometric Expressions
 Simplifying Trigonometric Expressions Using Trigonometric Identities
 Evaluating Trigonometric Functions Using Pythagorean Identities
 Evaluating Trigonometric Functions Using Periodic Functions
 Solving Equations Using Inverse Trigonometric Functions
 Solving Reciprocal Trigonometric Equations
 Simple Trigonometric Equations
 Solving a Trigonometric Equation
 Angle Sum and Difference Identities
 DoubleAngle and HalfAngle Identities
 Solving Trigonometric Equations Using Trigonometric Identities
 Solving Trigonometric Equations with the DoubleAngle Identity
 Modeling with Trigonometric Functions