In Problem use a graphing calculator as necessary to explore the graphs of the indicated cross sections.

Let f(x, y) = e^{-(x2 + y2)}.

(A) Explain why f(a, b) = f(c, d) whenever (a, b) and (c, d) are points on the same circle centered at the origin in the xy plane.

(B) Describe the cross sections of the surface z = f(x, y) produced by cutting it with the planes x = 0, y = 0, and x = y.

(C) Describe the surface z = f(x, y).