Answer to Question #234179 in Algebra for Hena

Question

Is x*y=0 a function?

Answer 1

It is not a function (as it was pointed out in a comment), but a relation, like a circle (a set of ordered pairs): R={(x,y)|xy=0}.

As a function of one variable it is not (in general) a function, indeed recall that by definition

$f:A⊆R→R\space\space∀x∈A\space∃!y\space y=f(x)$

x=0 we have that y can assume any value.

It would be a function, in implicit form, if we assume for example

f:R∖{0}→R

which correspons to the function y=0 with domain x≠0