functions - Why is the domain of x raised to x (0,infinity)?

My math teacher was explaining how to draw graphs of given functions. For $f(x)=x^x$ he put the domain as $(0,\infty)$. Why is this true (if it is)?
For $x= -2$, $(-2)^{-2}$ is $1/4$, and so the function is defined at $x= -2$. Isn't it?