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: Two-Way 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
- Two-by-Two Determinants
- Three-by-Three 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
- Double-Angle and Half-Angle Identities
- Solving Trigonometric Equations Using Trigonometric Identities
- Solving Trigonometric Equations with the Double-Angle Identity
- Modeling with Trigonometric Functions
