Is $f(x)={x}^{5/3}-5{x}^{2/3}$ defined over $(-\mathrm{\infty},0]$?

I've encountered this question: Find and describe all local extrema of $f(x)={x}^{5/3}-5{x}^{2/3}.$.

Also indicate on which regions the function is increasing and decreasing.

I've managed to find the extrema, but I am not sure whether the function is defined on $(-\mathrm{\infty},0]$. To make sure I looked on the internet at some graphing calculators and some of them graphed the function on that interval while others did not. Is it defined on that interval?

I've encountered this question: Find and describe all local extrema of $f(x)={x}^{5/3}-5{x}^{2/3}.$.

Also indicate on which regions the function is increasing and decreasing.

I've managed to find the extrema, but I am not sure whether the function is defined on $(-\mathrm{\infty},0]$. To make sure I looked on the internet at some graphing calculators and some of them graphed the function on that interval while others did not. Is it defined on that interval?