Answer
(a) $f\left( {x,y} \right) = xy$ matches contour graph (ii).
(b) $f\left( {x,y} \right) = {{\rm{e}}^{xy}}$ matches contour graph (i).
(c) $f\left( {x,y} \right) = \sin \left( {xy} \right)$ matches contour graph (iii).
Work Step by Step
We sketch the contour graphs of the functions (a)-(c) (please see the figure attached) and compare them with those in Figure 3. Thus, we obtain the following matches:
(a) $f\left( {x,y} \right) = xy$ matches contour graph (ii).
(b) $f\left( {x,y} \right) = {{\rm{e}}^{xy}}$ matches contour graph (i).
(c) $f\left( {x,y} \right) = \sin \left( {xy} \right)$ matches contour graph (iii).
