Characteristics and Properties of Functions

Advanced Functions
MHF4U1 (Grade 12 University Preparation)

Functions, domain and range

Concepts

  • definition of a function
  • function notation
  • definitions of domain and range
  • notation used for stating domain and range
  • domain issues resulting from division by zero and square roots of negative numbers

Absolute Value

Concepts

  • definition of absolute value
  • evaluating expressions involving absolute value
  • using a number line to represent equations/inequalities involving absolute value
  • the absolute value function
  • applying transformations to the graph of the absolute value function

Teacher Resources

Properties of Functions

Concepts

  • describing functions
  • domain and range
  • intervals of increase and decrease
  • absolute extreme values
  • local extreme values
  • continuity
  • symmetry
  • end behaviour

Inverse Relations

Concepts

  • definition of inverse relation
  • inverse function notation
  • equations of inverse relations
  • graphs of inverse relations

Teacher Resources

Piecewise Functions

Concepts

  • definition of piecewise function
  • graphs of piecewise functions
  • equations of piecewise functions
  • modelling with piecewise functions
  • continuity with piecewise functions

Teacher Resources

Exploring Operations with Functions

Concepts

  • adding, subtracting and multiplying functions
  • graphs involving operations with functions
  • equations involving operations with functions
  • domains of sums, differences and products of functions

Teacher Resources

Unit Review

Concepts

  • review of all concepts covered in the Characteristics and Properties of Functions unit

Teacher Resources