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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 :)

Ranc
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John Hon
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  • May be the website computes $x^x$ by $e^{x\ln x}$. – velut luna Oct 23 '16 at 12:50
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    $(-1)^{-1}$ is "easier" to compute than $(-0.5)^{-0.5}$ since the latter requires the introduction of complex numbers. Are you familiar with them? – Ranc Oct 23 '16 at 12:52
  • The resemblence to $\exp(x)$ originiates from the scaling of the graph ($e^x$ looks like $1+x$ near $0$). Try to plot it side by side and you'll notice an astnoshing difference. – Ranc Oct 23 '16 at 13:04
  • This may be relevant: http://math.stackexchange.com/questions/394110/can-the-graph-of-xx-have-a-real-valued-plot-below-zero – Michael Hoppe Oct 23 '16 at 18:52

1 Answers1

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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.

adjan
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