This document defines and describes relations and functions. It explains that a relation is a set of ordered pairs, graph or rule with domains and ranges. Relations can be one-to-one, many-to-one, one-to-many, or many-to-many. A function is a special type of relation that is many-to-one, where a vertical line can only cross the graph once. Functions can be one-to-one or many-to-one, and a one-to-one function's inverse is its reflection across the line y=x.

1. Maths Methods
Relations and Functions
REVISION

2. Relations and Functions
Relation: a listed set of ordered pairs, a
graph or a rule with specified or implied
domains
Domain: set of all x-values
Range: set of all y-values

3. Relations and functions
Four types of relations
One-to-one: one x-value to one y-value
Many-to-one: more than one x-value is
mapped to the same y-value
One-to-many: one x-value is mapped to
more than one y-value
Many-to-many: more than one x-value is
mapped to more than one y-value

4. Relations and functions
Function: A many-to-one relation. The
graph cannot be crossed more than once
by a vertical line drawn anywhere on the
graph.

5. Relations and functions
Two types of functions:
One-to-one: Graph can be crossed only once
by any vertical or horizontal line
Many-to-one: Graph can be crossed only
once by a vertical line.
The domain of many-to-one functions can be
restricted to make one-to-one functions.

6. Relations and functions
Inverse function is the reflection of a
one-to-one function in the line y=x
A function has an inverse function if it
is a one-to-one function
The original function and its inverse
intersect on the line y=x

7. Relations and functions
Resources
Video: 283_one-to-one functions
Worksheet: Functions