I plotted $y=x^x$ just for fun online, but i cam up with very confusing and unexpected results. The returned graph resembles a form of exponential, but with some unique features. They are the reasons why i'm confused. Graphs seem to be able to graph positive $x$-axis perfectly, but the negative $x$-axis is empty, which seems strange. Surely $(-1)^{-1}$ can be figured out right? So what is stopping the graph completing the whole thing?
Thank you for your time :)
The plotter can't plot complex valued functions. $(-n)^{-n}$ can obviously be figured out in the reals, but for every other $x\in \mathbb{R^-}$ the expression evaluates to a complex number, eg. for $x = -\frac 1 2$ we have ${(-\frac 1 2 })^{- \frac 1 2} = \frac 1 {\sqrt{-\frac 1 2}}= -i\sqrt{2}$.
Wolfram Alpha, for example, can plot the correct graph, see here.