College Algebra

Relations and Functions Video Review Lessons

Graphing Basics
• Using the Cartesian System
• Thinking Visually
Relationships between Two Points
• Finding the Distance between Two Points
• Finding the Second Endpoint of a Segment
Relationships among Three Points
• Collinearity and Distance
• Triangles
Circles
• Finding the Center-Radius Form of the Equation of a Circle
• Finding the Center and Radius of a Circle
• Decoding the Circle Formula
• Solving Word Problems Involving Circles
Graphing Equations
• Graphing Equations by Locating Points
• Finding the x- and y-Intercepts of an Equation
Function Basics
• Functions and the Vertical Line Test
• Identifying Functions
• Function Notation and Finding Function Values
Working with Functions
• Determining Intervals Over Which a Function Is Increasing
• Evaluating Piecewise-Defined Functions for Given Values
• Solving Word Problems Involving Functions
Function Domain and Range
• Finding the Domain and Range of a Function
• Domain and Range: One Explicit Example
• Satisfying the Domain of a Function
Linear Functions: Slope
• An Introduction to Slope
• Finding the Slope of a Line Given Two Points
• Interpreting Slope from a Graph
• Graphing a Line Using Point and Slope
Equations of a Line
• Writing an Equation in Slope-Intercept Form
• Writing an Equation Given Two Points
• Writing an Equation in Point-Slope Form
• Matching a Slope-Intercept Equation with Its Graph
• Slope with Parallel and Perpendicular Lines
Linear Functions: Applications
• Constructing Linear Function Models of a Set of Data
• Linear Cost and Revenue Functions
Graphing Functions
• Graphing Some Important Functions
• Graphing Piecewise-Defined Functions
• Matching Equations with Their Graphs
The Greatest Integer Function
• The Greatest Integer Function
• Graphing the Greatest Integer Function
Composite Functions
• Using Operations on Functions
• Composite Functions
• Components of Composite Functions
• Finding Functions That Form a Given Composite
• Finding the Difference Quotient of a Function
Quadratic Functions: Basics
• Deconstructing the Graph of a Quadratic Function
• Nice-Looking Parabolas
• Using Discriminants to Graph Parabolas
• Maximum Height in the Real World
Quadratic Functions: The Vertex
• Finding the Vertex by Completing the Square
• Using the Vertex to Write the Quadratic Equation
• Finding the Maximum or Minimum of a Quadratic
• Graphing Parabolas
Manipulating Graphs: Shifts and Stretches
• Shifting Curves along Axes
• Shifting or Translating Curves along Axes
• Stretching a Graph
• Graphing Quadratics Using Patterns
Manipulating Graphs: Symmetry and Reflections
• Determining Symmetry
• Reflections
• Reflecting Specific Functions