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For example, the level curve of a function that takes two variables ($x$ and $y$ for example) and a parametric equation involving two functions ($x=f(t)=...$ and $y=g(t)=...$). Both of the resulting graphs would be in two dimensional space I believe.

Both of these ideas involving forming a graph determined by a single variable.

I think there is some fundamental difference that I seem to be missing. I've been thinking about this for a long time but maybe my line of thought is in the wrong direction, any help is appreciated.

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  • $\begingroup$ When you say "a function that takes two variables," I think of something like this: $f(x,y) = x^2 + y.$ How do you graph such a thing in a two-dimensional space? Instead, such functions are often graphed as a curved surface in three dimensions, using the rule $z=f(x,y).$ Did you mean instead a function of one variable graphed by the rule $y=f(x)$? It may help if you provide some examples that you have encountered. $\endgroup$ – David K Apr 11 at 14:27
  • $\begingroup$ @DavidK Thank you for the response! Apologies, I was talking about something like $f(x,y)=x^2+y$, which would indeed have to be graphed in three-dimensional space. From what you said and some searching I realized I'm thinking of something called level curves. I think that makes more sense, sorry for the mix up $\endgroup$ – James Ronald Apr 11 at 14:30
  • $\begingroup$ That is a much better question. $\endgroup$ – David K Apr 11 at 14:41
  • $\begingroup$ Read this: math.stackexchange.com/questions/1251457/… $\endgroup$ – Christian Blatter Apr 11 at 18:39
  • $\begingroup$ Did that answer (or the other answer to math.stackexchange.com/questions/1251457/…) clear up the issues? $\endgroup$ – David K Apr 12 at 12:22

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