A relation is a set of (x,y) coordinates. When each x value corresponds with exactly one y value, the relation is a function. Below we will provide examples of relations that are and are not functions.
A relation that is a function
Any set of ordered pairs in which each
x corresponds with exactly one
y is a function. Consider the following relation.
(-1,2),(3,5),(2,-3),(1,4),(5,-1)
Notice that each of the
x values
-1,3,2,1, and
5 each correspond with only one
y value. Thus, the relation is a function. Consider another relation:
(-1,2),(3,5),(2,-3),(1,4),(5,4)
Again, each
x value corresponds with exactly one
y value. Notice that the points
(1,4) and
(5,4) share the same
y value. The
y values do not affect if the relation is a function. In other words, it is okay for two
x values to share one
y value, as long as each
x value only correspond to one
y value. Thus, this relation is a function.
A relation that is not a function
A relation in which at least one x value corresponds to more than one y value is not a function. Consider the following relation.
(-1,2),(-1,5),(2,-3),(1,4),(5,-1)
Notice that the points (-1,2) and (-1,5) show that the x value -1 corresponds to more than one y value. Thus, the relation is not a function.