Wolfram Alpha's graphing

[pka]

\(\displaystyle y = x^{\tfrac{1}{3}} \ \ \ and \ \ \ y = \sqrt[3]{x} \ \) are equivalent, but WolframAlpha doesn't handle them the same.

See PLOT I PLOT II
Do you use WolframAlphaPro? That may be your confusion.

 

[lookagain]

The range of y = x^(1/3) for x < 0 is (-oo, 0), and the range of y = x - 4 for x < 0 is also (-oo, 0).

Given the product of these, the range of the given function is in Quadrant II.