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.
