Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 99: 108

See graph and explanations.

See graph; when $x\to-\infty, y\to0$ or $\lim_{x\to -\infty}sin(\frac{\pi}{x^2+1})=0$; while when $x\to\infty, y\to0$ or $\lim_{x\to \infty}sin(\frac{\pi}{x^2+1})=0$; the asymptote of the function is $y=0$