SOLUTION: Explain why the vetical line test can determine if a relation is a function or not. Does f(x) mean f times x when referring to the function? If not, what does f(x) mean?

Question 826595: Explain why the vetical line test can determine if a relation is a function or not. Does f(x) mean f times x when referring to the function? If not, what does f(x) mean?
Answer by josgarithmetic(39627) (Show Source): You can put this solution on YOUR website!
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.
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