Input value - |-0|1|2|1|0|
Output Value-|-4|-2|0|2|4|

how can I tell when anything is a function?

Im confused of this.
Help pleeaseee:o

A function assigns each element x of A exactly one element y of E.

Suppose we have a circle with radius 1. It has equation f(x)=\pm\sqrt{1-x^{2}}

If we plug in x=1/2, we get two different outputs.

\sqrt{1-(1/2)^{2}}=\frac{\sqrt{3}}{2}

-\sqrt{1-(1/2)^{2}}=-\frac{\sqrt{3}}{2}

See? Two different results for the same input. NOT a function.

Say we have f(x)=x^{2}. A parabola with vertex at (0,0).

If we have (6)^{2}=36, \;\ (-6)^{2}=36

This IS a function. See the difference?

Also, if we can pass a vertical line through its graph only once, then it is a function. A circle we can pass a vertical line through twice. Not a function.

The parabola x^2 we can only pass a vertical line through once. A function.



Google them and you'll find lots. Here's one: http://www.themathpage.com/aprecalc/functions.htm