How do you know if x=15 is a function?

1 Answer
Dec 19, 2017

It is not a function.

Explanation:

A function is essentially a map between x values and y values. That is, for any given x value there must be at most one possible y value. The set of x values for which there is a corresponding y value is called the domain of the function.

In our example, the only x value for which there are any y values is x=15, and then the y value is totally unrestricted. For example, both (15,0) and (15,1) belong to the set of (x,y) values satisfying the equation.

So x=15 does not define a function.

Another way of describing the condition above is that x=15 fails the vertical line test - the requirement that any vertical line intersects the graph in at most one point. This fails when x=15 because a vertical line at that point intersects the graph at infinitely many points.