Sketching graph in R3

Let , and let C be the curve of intersection of with the plane .

Sketch the graph of the curve C.

I know how to graph y = x in R3, but I am not sure how to graph z = f(x,y). Would you use the same steps as you would when sketching a graph in R2? (e.g. first, second derivatives, asymptotes etc).

Quote:

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Originally Posted by SyNtHeSiS

Let , and let C be the curve of intersection of with the plane . Sketch the graph of the curve C.

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The intersection is:



You can determine the position of drawing the curve, as usual.

Fernando Revilla

Thanks. I tried checking the graph on wolfram alpha and I dont get why when x < 0 the graph (real part) is negative. I mean if you let x = -2 in z = x^{2/3} you get a positive value.