Chapter 14.1, Problem 32E

Match the function with its graph (labeled I–VI). Give reasons for your choices.

(a) $f(x,y)=\frac{1}{1+x^2+y^2}$

(b) $f(x,y)=\frac{1}{1+x^2{y}^2}$

(c) $f(x,y)=\ln (x^2+y^2)$

(d) $f(x,y)=\cos \sqrt{x^2+y^2}$

(e) $f(x,y)=\left|xy\right|$

(f) $f(x,y)=\cos (xy)$