Question 826595
f(x) is a description of a set of numbers; f(x) is one set of numbers and x is the variable that produces a corresponding number, f(x).  The number, x, is an input variable, and the output variable is f(x).


If f(x) is a function, then each value of x gives no more than one value for f(x).  That is why the vertical line test works for classifying a relation as a function or not a function.  If a vertical line can be found which intersects the relation in more than one point, then the relation not a function.


Very simple examples:


CIRCLE:  A vertical line may intersect at two points.  A circle is not a function.


POLYNOMIAL:  Depending how it is oriented, if using x as the horizontal axis, and "y" as the vertical axis, any vertical line will intersect the relation in exactly one point.  A polynomial relation of this kind is a function.