- Distance Formula Introduction
- Midpoint Formula Introduction
- Graphing by Ordered Pairs
- Finding Intercepts
- Symmetry Lecture
- Graphing Key Equations
- Calculating and Interpreting Slope
- Graphing by Point-Slope and Vertical Lines
- Equations and Graph of a Line given Two Points
- Slope-Intercept Form and General Form of Lines
- Parallel and Perpendicular Lines
- Using Point-Slope Formula to Graph and Horizontal Lines
- Standard Form of a Circle and Graphing with Intercepts of a Circle
- General Form of a Circle
- Relations and Function Introduction
- Evaluating a Function
- Domain and Range of a Function
- Basic Operations of Functions
- Graph of a Function by the Vertical Line Test and identifying domain/range
- Even and Odd Functions
- Increasing, Decreasing and Constant Functions
- Maxima and Minima of Functions
- Average Rate of Change and Secant Lines
- Library of Functions - Identification and Evaluation
- Piece-wise defined functions - Graphs and Applications
- Transformations with Vertical and Horizontal Shifts
- Transformations with Horizontal and Vertical Compressions and Stretches
- Multiple Transformations and Summary
- Constructing graphs based on Transformations and Identification of Transformed Graphs
- Graphing and Average Rate of Change of Linear Functions
- Linear Functions regarding Increasing, Decreasing or Constant
- Linear Function Models and Applications
- Quadratic Functions and Equations and their zeros - part 1
- Quadratic Functions and equations and their zeros - part 2
- Quadratic Functions and Equations and their zeros - part 3
- Quadratic Inequalities
- Maximum or Minimum of a Quadratic Function
- Finding a Quadratic Function Given the Vertex and another point
- Quadratic Function Graphs using Vertex, Axis and Intercepts
- Quadratic Function Vertex and Axis of Symmetry Identification
- Quadratic Functions using Transformations
- Solving Absolute Value Inequalities
- Solving Absolute Value Equations
- Analyzing the Graph of a Polynomial Function
- Graphing Polynomial Functions using Transformations
- Real Zeros and Multiplicity of Polynomial Functions
- Definition of a Polynomial Function
- Remainder and Factor Theorem
- Descartes Rule of Signs
- Rational Zeros Theorem
- Real Zeros Example 1
- Real Zeros Example 2
- Intermediate Value Theorem
- Conjugate Pairs Theorem for complex zeros
- Finding Polynomial functions for given zeros
- Finding Complex Zeros of a Polynomial Function
- Definition and Forming of Composite Functions
- Finding the Domain of Composite Functions
- Breaking a Composite Function into Component Functions
- Rational Function with definition, Domain and Transformation
- Rational Function discussion of Vertical Asymptotes
- Rational Function discussion of Horizontal and Oblique Asymptotes
- Graphs of Rational Functions – Example 1
- Graphs of Rational Functions – Example 2
- Graphs of Rational Functions – Example 3 (Curvilinear – optional video)
- Graphs of Rational Functions – Example 4
- Graphs of Rational Functions – Example 5 (Holes – optional video)
- Graphs of Rational Functions – Example 6
- Determining whether functions are one to one & Horizontal Line Test
- Determining Inverse Functions based on mappings and Ordered Pairs
- Inverse Functions of One to One Functions using Graphs
- Finding Inverse Functions defined by an equation
- Exponential Functions - Definition, Laws, and Evaluating
- Graphing Exponential Functions
- The Euler Function (the number "e")
- Solving Exponential Equations
- Logarithmic Functions Discussion
- Exponential and Logarithmic Function Conversion
- Evaluating Logarithmic Expressions
- Domain of Logarithmic Functions
- Graphs of Logarithmic Functions
- Solving Logarithmic Equations
- Basic Properties of Logarithms
- Expanding Logarithmic Expressions using Laws of Logarithms
- Simplifying a Logarithmic Expressions using Laws of Logarithms
- Evaluating Logarithms and Change of Base Theorem
- Solving Exponential and Logarithmic Equations with Same Bases
- Solving Exponential Equations with Different Bases
- Definition of Angles and Degree forms with Radian Introduction
- Arc Length, & Radian-Degree Conversion
- Area of a Sector of a Circle
- Definition of trigonometric functions using Right Triangles
- Development of the Fundamental Identities
- Using Trigonometric functions to find other trigonometric functions
- Cofunctions by way of the Complementary Angle Theorem
- Trigonometric Functions evaluated at 45°
- Trigonometric Functions Evaluated at 30° degrees and 60°
- Finding Exact Values of any Angle for Trigonometric Functions
- Using a Calculator to Evaluate Trigonometric Functions
- Models and Applications involving Right Triangles
- Coterminal Angles to find Exact Values of a Trigonometric Function
- Determining the Signs of Trigonometric Functions based on Quadrant Location
- Finding the Reference Angle of a Given Angle
- Using Reference Angles to Evaluate Trigonometric Functions
- Finding Exact Values of Trigonometric Functions given additional information
- Exact Values of Inverse Sine Functions
- Approximate Values of Inverse Sine Functions
- Properties of Inverse Trigonometric Functions to Evaluate for Exact Values
- Finding the Inverse of a Trigonometric Function
- Solving Inverse Trigonometric Equations
- Establishing Trigonometric Identities
- Using Algebra to Simplify Trigonometric Expressions
- Definition of an Identity and Review of Fundamental Identities
- Solving Trigonometric Equations using Fundamental Identities
- Solving Trigonometric Equations Quadratic in Form
- Solving Trigonometric Equations Using a Calculator
- Solving Trigonometric Equations with one trigonometric function
- Writing Trigonometric Expressions to Algebraic Expressions
- Evaluating Inverse Secant, Cosecant, and Cotangent Functions with Calculator
- Definition of Inverse Secant, Cosecant, and Cotangent Functions
- Exact Values of Inverse Sine, Cosine, and Tangent Functions
- Finding Exact Values of Trigonometric Functions Using Even-Odd Properties
- Using Sum/Difference formulas to find exact values
- Using Double-Angle Identities to Establish Identities & Intro to Tangent Double Angle Formula
- Using Double-Angle Formulas to Find Exact Values
- Graphing Sine/Cosine with non-standard period and phase shift
- Solving Right Triangles
- Application Modeling for Right Triangles
- Law of Sines Introduction and SSA-ASA Triangles
- Law of Sines - SSA (The Ambiguous Case)
- Law of Sines Application Models
- Law of Cosines Introduction and SAS Triangles
- Law of Cosines - SSS Triangles
- Law of Cosines Application Models
- Area of Triangles Introduction and Sine Area Formula
- Area of Triangles Using Heron's Formula
- Using Sum/Difference Formulas to Verify Identities
- Sum/Difference Formulas involving Inverse Trigonometric Functions
- Solving Sine/Cosine Equations linear in form
- Finding Exact Values of Trigonometric Functions Using Period Properties
- Domain and Range of Trigonometric Functions
- Using Unit Circle to find exact values of Trigonometric Functions
- Graphs of Sine Function with phase shift zero
- Graph of Cosine Function with phase shift zero
- Finding amplitude and period of Sine and Cosine Functions
- More Graphs of Sine and Cosine Functions Using Key Points
- Finding the Equation of a Sinusoidal Graph
- Graphs of Tangent and Cotangent with zero phase shift
- Graphs of Secant and Cosecant Function with Phase Shift zero
- Vectors Introduction and New Terminology
- Parallel Vectors
- Finding a Vector from its Direction and Magnitude
- Finding a Unit Vector in Algebraic or Linear Combination Form
- Finding a Scalar Multiple and the Magnitude of a Vector
- Finding a Positional Vector Using Algebraic or Component vector Form
- Dot Product of Two Positional Vectors
- Combining Vectors using Graphs
- Angles between two Positional Vectors
- Adding and Subtracting Vectors in Algebraic Form
- Orthogonal Vectors