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Suppose we have a function with two variables $x, \ y$, ie $f(x,y)=z$

Is there any universal, general way of determining the projection of the graph of this function, after intersecting it with a plane, onto $xy$ plane?

I'm having some trouble finding it on the web.

Could you help me with this issue?

For example, we are given a paraboloid $x^2 + y^2 = z$ and a plane $z = 3y$ or a cylinder $x^2 + y^2 = 4$. What is the eficient way of finding the projection of intersection of two of the above?

I'm sorry for the confusion.

Thank you in advance!

Bilbo
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    What do you mean by "the projection of a function"? (Perhaps the projection of the graph?) And when you say "a function with three variables", do you mean "$w = f(x, y, z)$" (i.e., a function of three variables) or "$z = f(x, y)$"? If the latter (as I suspect), the projection is just the domain of $f$.... – Andrew D. Hwang Sep 15 '14 at 11:50
  • I've edited my question. I hope it's more clear now. – Bilbo Sep 15 '14 at 11:57

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