Maths MethodsRelations and Functions

K McMullen 2011

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

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

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

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

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

Relations and Functions

Resources

Video: 283_one-to-one functions

Worksheet: Functions

K McMullen 2011