Mystery understanding different graphs of rational function $y = (x-4)^{2/3}$ $y = (x-4)^{2/3}$ is simple enough, right?  By inspection, a cusp function with cusp at $(4,0)$ and a $y$ intercept of $16^{.333} = 2.52$, but...
When graphed on Desmos the above is what I see.
When graphed on Fooplot, only the right side of the cusp is shown.
When graphed on wolfram, at $x<0$, real part is negative and there is an imaginary part that I can't understand.
Can someone share their insight with me?

Generally function $g(y)=y^a$, where $a$ is a positive constant, is well-defined for $y\geq0$. Hence your function is well-defined for $x\geq4$. For the other case, one may take additional assumptions  and they are different in your programs, hence different results.
