Question

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

Answer 1

To solve the problem we are given a function $x=15$, to know given equation is function or not .For that we have to check that is, for any given $x$ value there should be a corresponding y value. By checking it we can say whether a given equation is a function or not.

Complete step by step answer:
For the given problem we are given to prove that whether $x=15$ is a function. As we know that Functions are relations that derive one output for each input, or one y-value for any x-value inserted into the equation. Function is an essentially map between $x$and $y$values. That is, for any given $x$ value there should be a corresponding y value.
For checking whether a given equation is function or not we have to examine the ordered pairs. An ordered pair is a point on an x-y​coordinate graph with an x and y-value. For example, $\left( -2,2 \right)$ is an ordered pair with 2 as the x​-value and −2 as the y-value.
Now for 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 $\left( 15,0 \right)$ and $\left( 15,1 \right)$ belong to the set of $\left( x,y \right)$ values satisfying the equation.
So, therefore $x=15$ does not define a function.

Note:
We can solve this problem by another way i.e. vertical line test. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.