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MHF4U - Grade 12 Advanced Functions Videos (Ontario)
1.1 - Functions
REVIEW - relations, domain and range (video)
REVIEW - functions and vertical line test (video)
finding domain and range from table of values or coordinates
finding domain and range from mapping diagram
finding domain and range from a graph
finding domain and range from algebraic expressions part 1
finding domain and range from algebraic expressions part 2
relations and functions example 1
Finding Domain and Range from Complex Graph Example 1 (video)
Finding Domain and Range from Complex Graph Example 2 (video)
Finding Domain from Complex Functions Example 1 (video)
Finding Domain from Complex Functions Example 2 (video)
Finding Domain from Complex Functions Example 3 (video)
Finding Domain from Complex Functions Example 4 (video)
Draw Relation given Characteristics (video)
1.2 - Absolute Value
REVIEW - Absolute Value Function Overview (video)
absolute value inequalities part 1 (video)
absolute value inequalities part 2 (video)
Advanced Absolute Value Function 1 (video)
Advanced Absolute Value Function 2 (video)
Advanced Absolute Value Function 3 (video)
Advanced Absolute Value Function 4 (video)
1.3 - Properties of Functions
intervals of increase and decrease (6:01)
Intervals of Increase vs Decrease Breakdown (PDF)
symmetry (odd vs even) (6:07)
symmetry (odd vs even) example (video) (8:14)
How Can We Make a Quadratic Even?? (video)
Advanced Symmetry (odd vs even) Example 1 (video)
Advanced Symmetry (odd vs even) Example 2 (video)
Advanced Symmetry (odd vs even) Example 3 (video)
Advanced Symmetry (odd vs even) Example 4 (video)
Advanced Symmetry (odd vs even) Example 5 (video)
Advanced Symmetry (odd vs even) Example 6 (video)
Advanced Symmetry (odd vs even) Example 7 (video)
continuity and discontinuity (3:22)
end behaviours (4:44)
characteristics of parent functions (video) (11:59)
characteristics of sin(x) (video) (11:50)
Sketching Function given Characteristics Example 1 (PDF)
Sketching Function given Characteristics Example 2 (PDF)
quiz (pdf)
quiz solutions (pdf and video) (11:57)
1.4 - Sketching Functions
Transformations of Functions Overview (video)
Vertical Stretch, Compression and Reflection in x-axis (video)
Horizontal Stretch, Compression and Reflection in y-axis (video)
Horizontal Translations (video)
Vertical Translations (video)
General Process for Graphing Overview (video)
Graphing Example 2 (video)
Graphing Example 3 (video)
Graphing Example 4 (video)
Graphing Example 5 (video)
Graphing Example 6 (video)
Transformations of Points Example 1 (video)
Transformations of Points Example 2 (video)
Write Equation Given Transformations Example 1 (video)
Write Equation Given Transformations Example 2 (video)
Graph Radical Function Presented in Different Format (video)
Tricky Transformation Problem with Exponential Function (video)
1.5 - Inverse Relations
REVIEW - Inverse of a Function Overview (video)
REVIEW - Inverse of a Function Example 1 (video)
REVIEW - Inverse of a Function Example 2 (video)
REVIEW - Inverse of a Function Example 3 (video)
REVIEW - Inverse of a Function Example 4 (video)
REVIEW - Inverse of a Function Example 5 (video)
REVIEW - Inverse of a Function Example 6 (video)
REVIEW - Inverse of a Function Example 7 (video)
Finding Inverse for Functions Example (video)
Find Inverse of a Function Formula (video)
Find the Inverse of a Standard Form Quadratic (video)
Inverse of a Function Communication Problem 1 (video)
Inverse of a Function Communication Problem 2 (video)
1.6 - Piecewise Functions
piecewise functions overview with example 1 (9:15)
piecewise functions example 2 (7:01)
piecewise functions example 3 (10:52)
piecewise functions example 4 (4:28)
piecewise functions example 5 (4:08)
quiz (pdf)
quiz solutions (pdf and video) (16:37)
Find Constants to Make Function Continuous (video)
1.7 - Operations with Functions
operations with functions 1 (video) (6:29)
operations with functions 2 (video) (8:28)
Unit 1 - Test 1
Test 1 Questions (pdf)
Knowledge Question 1 Soluition (video)
Knowledge Question 2 Soluition (video)
Knowledge Question 3 Soluition (video)
Knowledge Question 4 Soluition (video)
Knowledge Question 5 Soluition (video)
Application Question 1 Solution (video)
Application Question 2 Solution (video)
Application Question 3 Solution (video)
Application Question 4 Solution (video)
Application Question 5 Solution (video)
Thinking Question 1 Solution (video)
Thinking Question 2 Solution (video)
Thinking Question 3 Solution (video)
Thinking Question 4 Solution (video)
Thinking Question 5 Solution (video)
Communication Question 1 Solution (video)
Communication Question 2 Solution (video)
Communication Question 3 Solution (video)
Communication Question 4 Solution (video)
Communication Question 5 Solution (video)
Unit 1 - Test 2
Test 1 Questions (pdf)
Test 1 Solutions (pdf)
Knowledge Section Solutions (video)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
Unit 1 - Test 3
Test 2 Questions (pdf)
Test 2 Solutions (pdf)
Knowledge Section Solutions (video)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
2.1 - Determining Average Rate of Change
Average Rate of Change Overview (video)
Average Rate of Change from Table of Values (video)
Average Rate of Change from Equation (video)
Average Rate of Change from Graph (video)
Average Rate of Change Example 1 (video)
Average Rate of Change Example 2 (video)
Average Rate of Change Thinking Problem 1 (video)
Average Rate of Change Thinking Problem 2 (video)
Average Rate of Change Thinking Problem 3 (video)
2.2 - Instantaneous Rates of Change from Tables of Values and Equations
Instantaneous Rate of Change Overview (video)
Preceding/Following Method Overview (video)
Preceding/Following Method Example (video)
Centered Interval/Squeeze Method Overview (video)
Centered Interval/Squeeze Method Example (video)
Difference Quotient Overview (video)
Difference Quotient Example 1 (video)
Difference Quotient Example 2 (video)
Difference Quotient Example 3 (video)
Difference Quotient Example 4 (video)
Difference Quotient Example 5 - Surface Area of Cube (video)
Difference Quotient Example 6 - Surface Area of Sphere (video)
IROC Example - Student Sent (written)
Find Equation of Tangent Using Diff Quotient - Rational (video)
Find Equation of Tangent Using Diff Quotient - Radical (video)
2.4 - Creating Graphs using Rate of Change
Displacement vs Time Graphs (video)
Speed vs Time Graphs (video)
Rate of Change When Pouring Water in Container (video)
Rate of Change with Swimming Pool Example (video)
2.5 - Solving Problems Involving Rates of Change
Verifying Max and Min Values Overview (video)
Verifying Max and Min Values Example (video)
Tangents around Max and Min Values (video)
Unit 2 - Test 1
Test 1 Questions (pdf)
Test 1 Solutions (pdf)
Knowledge Section Solutions (video) (1:52)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
Unit 2 - Test 2
Test 2 Questions (pdf)
Test 2 Solutions (pdf)
Knowledge Section Solutions (video)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
3.1 - Exploring Polynomial Functions
What is a Polynomial Function? (video)
Polynomial Functions and Constant Differences (video)
Constant Differences Example (video)
3.2 - Characteristics of Polynomial Functions
Polynomial Functions and End Behaviour (video)
Polynomial Functions and End Behaviour Breakdown (PDF)
Polynomial Functions and x-Intercepts (video)
Polynomial Functions and Turning Points (video)
Domain and Range of Polynomial Functions (video)
Drawing a Polynomial given Characteristics (video)
3.3 - Characteristics of Polynomial Functions in Factored Form
Polynomial Functions in Factored Form (video)
Finding the Degree of a Factored Polynomial (video)
Finding the Leading Coefficient in a Factored Polynomial (video)
Finding the y-intercept in a Factored Polynomial
Graphing Factored Polynomials Example 1 (video)
Graphing Factored Polynomials Example 2 (video)
Factored Polynomials and x-intercepts with Order (video)
Creating Polynomial Equation given x-intercepts Example 1 (video)
Creating Polynomial Equation given x-intercepts Example 2 (video)
Creating Polynomial Equation given Complex Roots (video)
Symmetry of Factored Form (odd vs even) Example 1 (video)
Symmetry of Factored Form (odd vs even) Example 2 (video)
Symmetry of Factored Form (odd vs even) Example 3 (video)
Symmetry of Factored Form (odd vs even) Example 4 (video)
How Can We Make a Quadratic Even?? (video)
Extra Problems for Symmetry Polynomials (PDF)
Tricky Factored Polynomial Question with Transformations (video)
Graph 5th Degree Polynomial with Characteristics (video)
Thinking Problem Dealing with Factored Polynomials (video)
3.4 - Transformations of Cubic and Quartic Functions
X-intercepts of Cubic vs Quartic Function (video)
3.5 - Dividing Polynomials
Long Division of Polynomials Overview (video)
Long Division of Polynomials Example 1 (video)
Long Division of Polynomials Example 2 (video)
Long Division of Polynomials Example 3 (video)
Long Division of Polynomials Example 4 (video)
Synthetic Division of Polynomials Overview (video)
Synthetic Division of Polynomials Example 1 (video)
Synthetic Division of Polynomials Example 2 (video)
Division of Polynomials Thinking Question (video)
3.6 - Factoring Polynomials
Remainder Theorem of Polynomials Overview (video)
Remainder Theorem of Polynomials Example 1 (video)
Remainder Theorem of Polynomials Example 2 (video)
Remainder Theorem of Polynomials Example 3 (video)
Find Two Constants with Remainder Theorem (video)
Factor Theorem of Polynomials Overview (video)
Rational Zero Theorem of Polynomials Overview (video)
Factoring Polynomials Example 1 (video)
Factoring Polynomials Example 2 (video)
Factoring Polynomials Example 3 (video)
When Two Polynomials Have Same Factor (video)
Tough Thinking Problem with Remainder Theorem (video)
Tough Thinking Problem with Factor Theorem (video)
Factoring + Volume of Cylinder Example (video)
Verifying Factors of a Polynomial Problem (video)
When Do Two Polynomials Have the Same Remainder? (video)
Finding Multiple Constants with Remainder Theorem (video)
Find Constants when a Quadratic is a Factor (video)
Find Constant with a Linear Divisor (video)
3.7 - Factoring a Sum or Difference of Cubes
Sum and Difference of Cubes Overview (video)
Sum and Differences of Cubes Example 1 (video)
Sum and Differences of Cubes Example 2 (video)
Sum and Differences of Cubes Example 3 (video)
Sum and Differences of Cubes Example 4 (video)
Sum and Differences of Cubes Example 5 (video)
Sum and Differences of Cubes Example 6 (video)
Sum and Differences of Cubes Example 7 (video)
Sum and Differences of Cubes Example 8 (video)
Sum and Differences of Cubes Tough Proof (video)
Simplify Expression with Difference of Cubes (video)
Unit 3 (Polynomial Functions) - Test 1
Polynomial Functions Test 1 Questions (pdf)
Polynomial Functions Test 1 Solutions (pdf)
Knowledge Section Solutions (video)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
Unit 3 (Polynomial Functions) - Test 2
Polynomial Functions Test 2 Questions (pdf)
Polynomial Functions Test 2 Solutions (pdf)
Knowledge Section Solutions (video)
Application Section Solutions (video)
Communication Section Solutions (video)
Thinking Section Solutions (video)
Unit 3 (Polynomial Functions) - Test 3
Polynomial Functions Test 3 Questions (pdf)
4.1 - Solving Polynomial Equations
Polynomial Equations Overview (video)
Why Does a Polynomial Equation Have No Solutions? (video)
Polynomial Equations and Volume Of A Box (video)
Finding Equation of Polynomial and Location of y value (video)
Finding Exact Values in Polynomial Equation (video)
4.2 - Solving Linear Inequalities
Linear Inequalities Overview (video)
Double Linear Inequality Example (video)
Is x=3 In The Solution Set For A Linear Inequality? (video)
4.3 - Solving Polynomial Inequalities
Polynomial Inequalities Overview (video)
Polynomial Inequality Example (video)
Tricky Polynomial Inequality (video)
Solving a Polynomial Inequality from Graph (video)
Find Polynomial Inequality When Given Solution (video)
Unit 4 (Polynomial Equations and Inequalities) - Test 1
Polynomial Equations and Inequalities Test 1 Questions (pdf)
Polynomial Equations and Inequalities Test 1 Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions
Thinking Section Video Solutions
Unit 4 (Polynomial Equations and Inequalities) - Test 2
Polynomial Equations and Inequalities Test 2 Questions (pdf)
Polynomial Equations and Inequalities Test 2 Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions
Thinking Section Video Solutions
Chapter 5 - Rational Functions ($40)
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Chapter 6 - Trigonometric Functions ($40)
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Chapter 7 - Trigonometric Identities and Equations ($40)
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Chapter 8 - Logarithmic and Exponential Functions ($40)
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Find Constants when a Quadratic is a Factor (video)
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