definition
A relation is simply a set of input and output values, represented in ordered pairs.
It is a relationship between sets of information.

A relation can be any set of ordered pairs.

No special rules need apply to a relation.

The following is an example of a relation:
{(1,1),(1,2),(3,3),(4,4),(5,5),(5,6),(6,4)}

NOTICE: In a relation, points can be plotted one above the other on a graph. The ordered pairs can have the x-values repeated, such as (1,1) and (1,2). The vertical line on the graph shows where this happens.

relation1
Relation:
{(
1,1),(1,2),(3,3),(4,4),(5,5),(5,6),(6,4)}

As seen above, a relation can be expressed in a graph,
and can be expressed in
set notation: {(1,1),(1,2),(3,3),(4,4),(5,5),(5,6),(6,4)}

Relations can also be expressed
in a
table:
x
y
1
1
1
2
3
3
4
4
5
5
5
6
6
4
Relations can also be expressed
in a
mapping diagram:

mappingdiagram

ex1

eye color
Consider this example of a relation:
The relationship between eye color and student names.
(x,y) = (eye color, student's name)


Set A = {(green,Steve), (blue,Elaine), (brown,Kyle), (green,Marsha), (blue,Miranda), (brown, Dylan)}
Notice that the x-values (eye colors) get repeated.



ex2

The graph we saw at the top of this page was a "scatter plot" which is comprised of a series of individual points, not connected.

A relation can also be a "connected" graph such as the graph shown at the right (a parabola).

This is the graph of the square root of x, assuming only values of 0 or larger are used for x.


relation2
Relation: relationmath1; allows for points
such as (
2,1.424) and (2,-1.414) or
(
4, 2) and (4,-2) .


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