# 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