Lesson 1: Functions

• Quick review of key terms:

  • Vertical line test

  • Transformation of a function

  • Domain and range of a function

  • Factoring expressions

• Defining key characteristics / properties of a function:

  • Intervals of increase / decrease

  • Odd and even functions

  • Continuous and discontinuous functions

  • End behaviour

  • Vertical and horizontal asymptote

• Determining end behavours

• Determination of these properties using examples

• Sketching graphs of functions

  • General equation of a transformed function

  • Description of x- and y- transformations

  • Solutions to worked examples

• Inverse of a relation

• Implications of reverse on the original function

• Defining Piecewise functions

  • Solution to a Piecewise function question

  • Solved application problems

Lesson 2: Operations with Functions

• Examples of solving operations with functions:

  • f(x) + g(x); f(x) – g(x); (f + g)(x); (f x g)(x); (f ÷ g)(x)

  • Solving (f + g)(x) within limits

  • Domain and range of (f + g)(x)

  • Determining table of values

  • Determining graphs of the functions

Here are a few sample questions for you to practice. The answers are given at the end.