Thanks, I thought it had something to do with binary relations.

I've also noticed that graphing such functions is quite difficult. I saw that you said that "

is a "paraboloid"." Can I guess the shape of a function by looking at the degree of the variables of the function i.e. would g(x, y) = x^3 + y^3 be some sort of hour-glass shape?

(Some background on these seemingly simple questions: I'm a first year physics student, I walked into the wrong lecture room and was too ashamed to get up in the middle of a class so I stayed and learned something about PDE's. Not much, but something... Partial derivatives actually make a lot of sense in the context of geometry- I would always get really pissed whenever I would encounter a related rates question in highschool calc involving geometry where a height variable would be held constant- now with partial differentiation I don't have to answer one part of the question... anyway, thanks)