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. 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 x-values (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) .