The graph of $x^x$

Question

I have a question about the graph of $f(x) = x^x$. How come the graph doesn't extend into the negative domain? Because, it is not as if the graph is undefined when $x=-5$. But according to the graph, that seems to be the case. Can someone please explain this?

Thanks

Answer 1

Well, for a START, what would happen if your exponents were to be -0.5, -1.5, -2.5, -3.5 etc? Convert that into radical notation and try to evaluate for those negative x-values. (And there is lots more going on for negative x-values)