$f(x):=x^{4/5}\cdot (x-4)^2$
Maple gives me the graph:
WolframAlpha gives this graph
and my calculator gives Error 2 if I plug in $(-1)^{4/5}$.
My original intuition would be to think that the graph would be defined for negative $x$, but clearly something else is going on, what is going on in this case?