Let $\displaystyle f(x,y) = x^{1/3}y^{1/3}$, and let C be the curve of intersection of $\displaystyle z = f(x,y)$ with the plane $\displaystyle y = x$.

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).