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
Relevant Links
Transformations Across Function Types
Concepts
- applying combinations of transformations to the graphs of various functions
- generalizing transformations using function notation
Relevant Links
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
Student Resources
Relevant Links
Properties of Functions
Concepts
- describing functions
- domain and range
- intervals of increase and decrease
- absolute extreme values
- local extreme values
- continuity
- symmetry
- end behaviour
Relevant Links
Inverse Relations
Concepts
- definition of inverse relation
- inverse function notation
- equations of inverse relations
- graphs of inverse relations
Student Resources
Relevant Links
Piecewise Functions
Concepts
- definition of piecewise function
- graphs of piecewise functions
- equations of piecewise functions
- modelling with piecewise functions
- continuity with piecewise functions
Student Resources
Relevant Links
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
Student Resources
Relevant Links
Unit Review
Concepts
- review of all concepts covered in the Characteristics and Properties of Functions unit