Slant asymptotes of $\sin x \times x/4$.

Question

I am aware, that by definition of a slant asymptote, we end up with a limit as $x$ approaches infinity of $\sin(x)/4$, which does not exist, but if we graph $\sin(x) \times (x/4)$, we may see that it approaches and touches $x/4$ and $-x/4$. Are those not asymptotes, or am I missing something? Thank you.