Asymptotes of a Composite Function

For the function $f$ defined by $f(x) = \sin\left(\displaystyle\frac{x+1}{x^2}\right)$, which of the following statements are true?

I. A horizontal asymptote exists at $y = 0$.

II. A horizontal asymptote exists at $y = 1$.

III. A vertical asymptote exists at $x = 0$.