Advanced Functions MHF4U — Grade 12 Math Lessons | PrepBox

Advanced Functions MHF4U — Grade 12

Explore Advanced Functions MHF4U for Grade 12. Follow the chapter and section outline to find available interactive lessons and video explanations. These are independent PrepBox learning resources; PrepBox is not affiliated with the textbook publisher.

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1,113 topic entries in the outline · 35 interactive entries · 848 video entries. Topics may appear in more than one section.

Chapter 1 Functions, Characteristics and Properties

1.0 Getting Started

1.1 Functions

1.2 Exploring Absolute Value

1.3 Properties of Graphs of Functions

Mid Chapter Review on Functions

1.4 Sketching Graphs of Functions

1.5 Inverse Function

1.6 Piecewise Function

  • Graph Piecewise Functions with Domain and Range · Video available
  • Find Linear Combination of Functions · Video available
  • Range of Absolute Value Functions · Not yet available
  • Find Piecewise Function from Points · Not yet available
  • Find Constants for Piecewise Continuity · Video available

1.7 Exploring Operations with Functions

Chapter Review

Chapter Practice Test on Functions

Chapter 2 Functions-Understanding Rates of Change

2.1 Determining Average Rates of Change

2.2 Estimating Instantaneous Rates of Change of Change from Tables of Values and Equations

2.3 Exploring Instantaneous Rates of Change Using Graphs

Mid Chapter Review

2.4 Using Rates of Change to Create a Graphical Model

2.5 Solving Problems Involving Rates of Change

Chapter Review on Rates of Change

Chapter Self Test

  • Find Average or Instantaneous Rate of Change · Video available
  • Find Average Rate of Change of a Function · Video available
  • Estimate Instantaneous Rate of Change from Word Problem · Not yet available

Chapter 3 Polynomial Functions

3.1 Exploring Polynomial Functions

3.2 Characteristics of Polynomial Functions

3.3 Characteristics of Polynomial Functions in Factored Form

3.4 Transformation of Cubic and Quartic Functions

Mid Chapter Review

3.5 Dividing Polynomials

3.6 Factoring Polynomials

3.7 Factoring a Sum of Differences of Cubes

Chapter Review on Polynomial Algebra

Chapter Practice Test on Polynomial Functions

Chapter 1 to 3 Cumulative Review

Chapter 4 Polynomial Equations and Inequalities

4.1 Solving Polynomial Equations

4.2 Solving Linear Inequalities

Mid Chapter Review

4.3 Solving Polynomial Inequalities

4.4 Rates of Change in Polynomial Functions

Chapter Review

Chapter Test Poly Inequality

Chapter 5 Rational Functions, Equations, and Inequalities

5.1 Graphs of Reciprocal Functions

5.2 Exploring Quotients of Polynomial Functions

5.3 Graphs of Rational Functions of the form f(x) = (ax + b)/(cx + d)

5.4 Solving Rational Equations

5.5 Solving Rational Inequalities

5.6 Rates of Change in Rational Functions

Chapter Review

Chapter Test

Chapter 6 Trigonometric Functions

6.1 Radian Measure

6.2 Radian Measure and Angles on the Cartesian Plane

6.3 Exploring Graphs of the Primary Trigonometric Functions

6.4 Transformations of Trigonometric Functions

Mid Chapter Review on Trig Functions

6.5 Exploring Graphs of the Reciprocal Trigonometric Functions

6.6 Modelling with Trigonometric Functions

6.7 Rates of Change in Trigonometric Functions

  • Find Average Rate of Change from Table · Video available
  • Find AROC of Trig Equation · Not yet available

Chapter Review

Chapter Test

Chapter 4 to 6 Cumulative Review

Chapter 7 Trigonometric Identities and Equations

7.1 Exploring Equivalent Trigonometric Functions

7.2 Compound Angle Formulas

7.3 Double Angle Formulas

7.4 Proving Trigonometric Identities

7.5 Solving Linear Trigonometric Equations

7.6 Solving Quadratic Trigonometric Equations

Chapter Review of Trig Identities and Equations

Chapter Test - Trig Identities and Equations

More Advanced Trig Identity Practice

Chapter 8 Exponential and Logarithmic Functions

8.1 Exploring the Logarithmic Function

8.2 Transformations of Logarithmic Functions

8.3 Evaluating Logarithms

Mid Chapter Review

8.4 Laws of Logarithms

8.5 Solving Exponential Equations

8.6 Solving Logarithmic Equations

8.7 Solving Problems with Exponential and Logarithmic Functions

8.8 Rates of Change in Exponential and Logarithmic Functions

Chapter Review for Logs

Chapter Test

Chapter 9 Combinations of Functions

9.1 Exploring Combinations of Functions

No named lesson topics are currently listed for this section.

9.2 Combining Two Functions - Sums and Differences

9.3 Combining Two Functions - Products

9.4 Exploring Quotients of Functions

9.5 Composition of Functions

9.6 Techniques for Solving Equations and Inequalities

  • Construct Functions With Prescribed Positivity and Relative Order · Not yet available
  • Solve Polynomial Equations (Find Zeros by Factoring) · Video available
  • Decompose Composite Function · Video available
  • Solve Trig Equation Using Double Angle Formula · Video available
  • Find an Exponent Using Logarithms · Video available
  • Graph Log and Exponential Together · Video available
  • Solve Equation or Inequality from Graph · Not yet available
  • Solve sqrt(quadratic) = linear · Video available
  • Solve Combined Functions Using Graphing Device · Not yet available
  • Solve Radical Equation Using Graphing · Not yet available

9.7 Modelling with Functions

Chapter Review

Chapter Test

No named lesson topics are currently listed for this section.

Chapter 7 to 9 Review