2

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.

James Ronald
  • 2,331
  • 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. – David K Apr 11 '19 at 14:27
  • @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 – James Ronald Apr 11 '19 at 14:30
  • That is a much better question. – David K Apr 11 '19 at 14:41
  • Read this: https://math.stackexchange.com/questions/1251457/what-is-parameterization/1251663#1251663 – Christian Blatter Apr 11 '19 at 18:39
  • Did that answer (or the other answer to https://math.stackexchange.com/questions/1251457/what-is-parameterization) clear up the issues? – David K Apr 12 '19 at 12:22

0 Answers0