This document discusses relations and functions in mathematics. It defines a relation as 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 many-to-one function's domain can be restricted to make it one-to-one. The inverse of a one-to-one function is its reflection over the line y=x.

1. Maths Methods
Relations and Functions
K McMullen 2011

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
K McMullen 2011

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
K McMullen 2011

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.
K McMullen 2011

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.
K McMullen 2011

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
K McMullen 2011

7. Relations and Functions
Resources
Video: 283_one-to-one functions
Worksheet: Functions
K McMullen 2011