Functions

Functions

Lesson 1: Relations and Functions
Lesson 2: Real Life Examples of Functions
Lesson 3: Definition of Functions
Lesson 4: Representing Functions with Ordered Pairs, Tables, and Equations
Lesson 5: Representing Functions with Graphs

Domain and Range of Functions

Lesson 1: Sets and Interval Notation Part 1
Lesson 2: Sets and Interval Notation Part 2
Lesson 3: Meanings of Domain and Range Part 1
Lesson 4: Meanings of Domain and Range Part 2
Lesson 5: Meanings of Domain and Range Part 3
Lesson 6: Meanings of Domain and Range Part 4 (from Graphs)
Lesson 7: Domain and Range of Radical Functions Part 1
Lesson 8: Domain and Range of Radical Functions Part 2
Lesson 9: Domain and Range of Radical Functions Part 3
Lesson 10: Domain and Range of Radical Functions (Summary)
Lesson 11: Domain and Range of Rational Functions Part 1
Lesson 12: Domain and Range of Rational Functions Part 2
Lesson 13: Domain and Range of Rational Functions Part 3
Lesson 14: Domain and Range of Absolute Value Functions Part 1
Lesson 15: Domain and Range of Absolute Value Functions Part 2
Lesson 16: Determining the Domain and Range of Functions from Graphs Part 1
Lesson 17: Determining the Domain and Range of Functions from Graphs Part 2
Lesson 18: Determining the Domain and Range of Functions from Graphs Part 3
Lesson 19: Domain and Range – More Examples Part 1
Lesson 20: Domain and Range – More Examples Part 2
Lesson 21: Domain and Range – More Examples Part 3

Linear Functions

Lesson 1: Introduction to Linear Functions
Lesson 2: Slope and Rate of Change
Lesson 3: Graphs of Linear Functions
Lesson 4: The effect of b in y = ax + b
Lesson 5: The Concept of Slope
Lesson 6: The Slope and y-intercept of Linear Functions
Lesson 7: Slope and Increasing or Decreasing Graphs
Lesson 8: Graphing Linear Functions Using Slope and y-Intercept
Lesson 9: Getting Equations of Graphs of Linear Functions
Lesson 10: Equations of Lines Given the Slope and a Point
Lesson 11: Equations of Lines Given Slope and y-intercept
Lesson 12: Equations of Lines Given Two Points Part 1
Lesson 13: Equations of Lines Given Two Points Part 2
Lesson 14: Equations of Lines Given Two Points Part 3

Quadratic Functions

Lesson 1: Introduction to Quadratic Function
Lesson 2: Graphing Quadratic Functions
Lesson 3: Graphing the Quadratic Function y = x^2
Lesson 4: The effect of a in y = ax^2 where a is greater than 0
Lesson 5: The effect of a in y = ax^2 where a is less than 0
Lesson 6: Properties of the quadratic function y = ax^2.
Lesson 7: Identifying Quadratic Functions from Tables
Lesson 8: Understanding Roots of Quadratic Functions
Lesson 9: Solving Roots of Quadratic Functions (2 Distinct Real Roots)
Lesson 10: Solving Roots of Quadratic Functions (2 Distinct Real Roots)
Lesson 11: Solving Roots of Quadratic Functions (2 Equal Real Roots)
Lesson 12:Solving Roots of Quadratic Functions (No Real Root)
Lesson 13: Discriminant of Quadratic Functions
Lesson 14: Deriving the Vertex Form of Quadratic Functions
Lesson 15: Quadratic Functions General Form to Vertex Form Example 1
Lesson 16: Quadratic Functions General Form to Vertex Form Example 2
Lesson 17: Quadratic Functions General Form to Vertex Form Example 3
Lesson 18: Solving for the x and y intercepts of Quadratic Functions Part 1
Lesson 19: Solving for the x and y intercepts of Quadratic Functions Part 2
Lesson 20: Graph Sketching Quadratic Functions Using Vertex And Intercepts

Polynomial Functions

Lesson 1: Introduction to Polynomial Functions
Lesson 2: Definition of Polynomial Functions
Lesson 3: Understanding the Name and Notation of Functions
Lesson 4: Understanding Zeroes of Polynomial Functions
Lesson 5: Finding the Zeroes of Polynomial Functions
Lesson 6: Finding the Values of a Polynomial Function
Lesson 7: Dividing Functions: Their Quotient and Remainder
Lesson 8: The Remainder Theorem
Lesson 9: Division of Polynomials Using Synthetic Division Part 1
Lesson 10: Division of Polynomials Using Synthetic Division Part 2
Lesson 11: Understanding the Factor Theorem
Lesson 12: Factor Theorem, Remainder Theorem, and Synthetic Division Part 1
Lesson 13: Factor Theorem, Remainder Theorem, and Synthetic Division Part 2
Lesson 14: Roots of Polynomial Functions
Lesson 15: Finding the Zeroes of a Polynomial Function by Factoring
Lesson 16: The Integral Zero Theorem
Lesson 17: Application of Integral Zero Theorem Part 1
Lesson 18: Application of Integral Zero Theorem Part 2
Lesson 19: Graphs of Polynomial Functions

Exponential Functions

Lesson 1: Introduction to Exponential Function
Lesson 2: Definition of Exponential Function
Lesson 3: Graphing Exponential Functions
Lesson 4: Examining Graphs of Exponential Functions Part 1
Lesson 5: Examining Graphs of Exponential Functions Part 2
Lesson 6: Exponential Functions with Reciprocal Bases

Operations on Functions

1. Introduction on How to Add, Subtract, Multiply, Divide Functions
2. The Effects of Operations on Functions to the Domain of the Resulting Function
3.) Addition of Functions – Worked Examples 1
4.) Addition of Functions – Worked Examples 2
5.) Addition of Functions – Domain of Sum Function
6.) Subtraction of Functions – Worked Examples 1
7.) Subtraction of Functions – Worked Examples 2
8.) Multiplication of Functions – Worked Examples 1
9.) Multiplication of Functions – Worked Examples 2
10.) Division of Functions – Worked Examples 1
11.) Division of Functions – Worked Examples 2

Composition of Functions

Lesson 1: Introduction to Composition of Functions
Lesson 2: Definition of Composition of Functions
Lesson 3: Composition of Functions – Worked Examples 1
Lesson 4: Composition of Functions – Worked Examples 2
Lesson 5: Composition of Functions – Worked Examples 3
Lesson 6: Composition of Functions – Worked Examples 4
Lesson 7: Composition of Functions – Worked Examples 5

Lesson 1: Introduction to Inverse Functions
Lesson 2: Mapping Inverse Functions
Lesson 3: Steps in Finding the Inverse Function
Lesson 4: Finding the Inverse of a Function – Worked Example 1
Lesson 5: Finding the Inverse of a Function – Worked Example 2
Lesson 6: Graphing Inverse Functions
Lesson 7: Functions without Inverses
Lesson 8: Relationship among Inverse Functions, Horizontal Line Test, and Vertical Line Test
Lesson 9: How to Verify if Two Functions are Inverses of Each Other