Plot of x^(1/3) has range of 0-inf in Mathematica and R Just doing a quick plot of the cuberoot of x, but both Mathematica 9 and R 2.15.32 are not plotting it in the negative space.  However they both plot x cubed just fine:
Plot[{x^(1/3), x^3}, 
    {x, -2, 2}, PlotRange -> {-2, 2}, AspectRatio -> Automatic]

http://www.wolframalpha.com/input/?i=x%5E%281%2F3%29%2Cx%5E3
plot(function(x){x^(1/3)} , xlim=c(-2,2), ylim=c(-2,2))

Is this a bug in both software packages, or is there something about the cubed root that I don't understand?
In[19]:= {1^3, 1^(1/3), -1^3, -1^(1/3), 42^3, -42^3, 42^(1/3) // N, -42^(1/3) // N}
Out[19]= {1, 1, -1, -1, 74088, -74088, 3.47603, -3.47603}

Interestingly when passing -42 into the R function I get NaN, but when I multiply it directly I get -3.476027.
> f = function(x){x^(1/3)}
> f(c(42, -42))
[1] 3.476027      NaN
> -42^(1/3)
[1] -3.476027


Really funny you'd mention that... my Calc professor talked about that last semester. ;)
Many software packages plot the principal root, rather than the real root. http://mathworld.wolfram.com/PrincipalRootofUnity.html
For example, $\sqrt[3]{3}$ has three values: W|A
Mathematica uses the roots in the upper-left quadrant when plotting the cube root.  Thus, it thinks it's complex, and therefore doesn't graph it.
