Let $$f(x) = \frac{ x }{ \sqrt[4]{x^4 + 2} }.$$ Find the horizontal and vertical asymptotes of $f(x)$. If there are no asymptotes of a given type, enter 'none'. If there are more than one of a given type, list them separated by commas.

Horizontal asymptote(s): $y$ =

Vertical asymptote(s): $x$ =