Chapter 14.1, Problem 32E

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

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

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

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

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

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

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