Implicitly Defined Function

I'm just doing some maths revision, and I've come across implicit differentiation, and I've just been wondering about the functions. Is it right to think that an implicitly defined function, just say xy^2 + yx^2 = 6, is still a function of x? It isn't a funtion of both x and y in the same way that, just say f(x,y):6xy +xy^2, is, is it? As in, an implicit function won't output a z co-ordinate, will it? Whereas a function f(x,y) will. Am I right in thinking that?

LeixlipRed

The implicit function you talk about is a function of one variable where it is impossible to explicitly isolate y. Assuming it still passes the vertical line test that is of course, i.e. if it's actually a function. An implicit function in one variable could be "converted" into a function of two variables by bringing all terms to one side of the equation and equating the expression to z or whatever. But they're totally different functions.

Thanks for your reply, yah that's kind of what I thought. Just wanted to be sure.

Thanks again.