Chapter 7.1, Problem 64E

In Problems 59–64, use a graphing calculator as necessary to explore the graphs of the indicated cross sections.

64. Let $f\left(x,y\right)=4-\sqrt{x^2+y^2}.$

1. (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.
2. (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.
3. (C) Describe the surface z = f(x, y).