Originally Posted by
Jhevon actually, it's if it cuts it more than once. why is that? a function is a relation in which each element in the domain (the set of inputs) maps to one and ONLY one element in the range (the set of outputs).
if we have a relation with x-values as the inputs, in which a vertical line cuts the graph of the relation at more than one point, it means there is some input (x-value) that has more than one output (y-value) and is therefore not a function.
look at the graph that we have for this problem (see below).
note that any vertical line drawn of the form x = c, where c is a constant greater than -1, will cut the graph twice. thus this is NOT a function, since it fails the vertical line test
alternatively, we could say that the x-value, x = 0 (for example) maps to two y-values, (y = 1, and y = -1) thus we have a one-to-many relation which is not a function (functions are one-to-one or many-to-one relations)