

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 xvalues repeated, such as (1,1) and (1,2). The vertical line on the graph shows where this happens.

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:


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 xvalues (eye colors) get repeated. 
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.

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

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