
Densely (un)Defined Function
A graph of the function x^{x}; although the graph does not
immediately appear to be a function, closer examination
will reveal its true nature. Most graphing programs do not define the exponential function for negative bases.
For negative x, x^{x} is
 undefined if x is irrational,
 undefined if x = odd / even,
 a welldefined positive real number if x = even / odd, and
 a welldefined negative real number if x = odd / odd.


