Match the function with its graph (labeled I - VI). Give reasons for your choices.
(a) $ f(x, y) = \dfrac{1}{1 + x^2 + y^2} $
(b) $ f(x, y) = \dfrac{1}{1 + x^2y^2} $
(c) $ f(x, y) = \ln(x^2 + y^2) $
(d) $ f(x, y) = \cos\sqrt{x^2 + y^2} $
(e) $ f(x, y) = | xy | $
(f) $ f(x, y) = \cos(xy) $