# 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