Something like this?
ParametricPlot3D[{x, Re[x^x], Im[x^x]}, {x, -1, 1}, AxesLabel -> {x, Re[x^x], Im[x^x]}]
Thanks to both of you, this helps a lot. However, if I want to very explicitly state the range for all of the axes, I still only know how to do this for the x (input) axis. How could I use that notation to specifically control the Im(x^x) and Re(x^x) ranges that are shown?
BoxRatio gives better view for large x
ParametricPlot3D[{x, Re[x^x], Im[x^x]}, {x, -10, 10}, AxesLabel -> {x, Re[x^x], Im[x^x]}, PlotRange -> All, BoxRatios -> {1, 1, 1}]
The plot is clipped. Simply adjust the PlotRange:
ParametricPlot3D[{x, Re[x^x], Im[x^x]}, {x, -3, 2}, AxesLabel -> {x, Re[x^x], Im[x^x]}, PlotRange -> All]
Yes, that works wonderfully! However, take a look at this:
Notice that, somewhere between 0 and -1 for x as the real input, it appears that part of the graph is missing. I believe (but am not confident) that the function should be continuous in that missing section and that the reason I'm not seeing it is because the secondary Y imaginary output axis Im(x^x) is so small that it doesn't include some of the output values. The axis range appears to be automatically determined depending on what I put in for the x range (in the picture I have x go from -3 to 2). How would I create a set value range for all three axis? It seems that I can only choose a range for the x-axis in the example you've given me.
