y =
x^(1/x)
has a pretty funky looking graph,
which rises sharply in the positive quadrant 1 then slowly decreases and then asymptotes to the x axis as x increases.
eg.
y = (1)^(1/1)= 1.0
y = (2)^(1/2)= 1.41421...
(square root of 2)
y = (3)^(1/3)= 1.4422...
(cubed root of 3)
y = (4)^(1/4)= 1.41421...
(the square root of the square root of 2 all squared, as it were.)
y = (5)^(1/5)= 1.3797...
y = (6)^(1/6)= 1.348...
and so on and so forth, to the nth root of n.