MHF4U: Advanced Functions

We will be using the workbook Advanced Functions 12 by McGraw-Hill Ryerson. Treat your textbook well — a replacement costs $100.

Topics Covered

  1. Polynomial Functions
    1. Unit Outline
    2. Review of Factoring Techniques | Worksheet
    3. factoring Sums and Differences of Cubes | Worksheet
    4. Domain and Range, Interval Notation | Worksheet
    5. Polynomial and Power Functions
    6. Characteristics of Polynomial Functions
    7. Equations and Graphs of Polynomial Functions
    8. Transformations of Polynomial Functions
    9. Average Rate of Change
    10. Instantaneous Rate of Change
  2. Polynomial Equations and Inequalities
    1. Unit Outline
    2. Polynomial Division | Worksheet
    3. Remainder Theorem
    4. Factor Theorem
    5. Descartes’ Rule of Signs | Worksheet
    6. Solving Polynomial Equations | Worksheet
    7. Families of Polynomials
    8. Linear Inequalities
    9. Solving Polynomial Inequalities
  3. Rational Functions
    1. Unit Outline
    2. Reciprocal of a Linear Function
    3. Reciprocal of a Quadratic Function
    4. Rational Functions of the Form (ax+b)/(cx+d)
    5. Oblique Asymptotes | Worksheet
    6. Rational Inequalities: Simple Examples
    7. Rational Inequalities: Complex Examples
  4. Trigonometric Functions
    1. Unit Outline
    2. Radian Measure
    3. Exact Values of Trigonometric Ratios
    4. Primary Trigonometric Functions
    5. Secondary Trigonometric Functions
    6. Transformations of Sinusoidal Functions
    7. Solving Trigonometric Equations
    8. Applications of Sinusoidal Functions
  5. Trigonometric Identities
    1. Unit Outline
    2. Basic Trigonometric Identities
    3. Cofunction and “Shifting” Identities
    4. Addition and Subtraction Identities
    5. Double and Half Angle Identities
    6. Solving Trigonometric Equations Using Identities
  6. Exponential and Logarithmic Functions
    1. Unit Outline
    2. Exponential Functions and Their Inverses
    3. Logarithmic and Exponential Equations
    4. Transformations of Logarithmic Functions
    5. Properties of Logarithms
    6. Solving Exponential Equations
    7. Solving Logarithmic Equations
    8. Applications of Exponential Functions
    9. Applications of Logarithmic Functions
  7. Combinations of Functions