Gradient

Consider the function f defined by
1) f(x,y) = 0 unless x>0 and
2) for each x > 0
3) for all (x,y) with x>0

Modify this to get a function g with



yet there is no direction of maximal change.

I know f has no direction of maximal change because and are both 0, and so the gradient is zero and the angle between the gradient and any direction vector is undefined. How can this happen when the gradient is 1?