Question

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

Answer 1

Hint: 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.