## 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

## Teacher Resources

## Transformations Across Function Types

## Concepts

- applying combinations of transformations to the graphs of various functions
- generalizing transformations using function notation

## 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

## Other Resources and 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

## Teacher Resources

## Other Resources and Links

## Inverse Relations

## Concepts

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

## Teacher Resources

## Other Resources and Links

## 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

## Other Resources and 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

## Teacher Resources

## Other Resources and Links

## Unit Review

## Concepts

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