Let's find the asymptotes of $\frac{x^3}{x^4+1}$, for real $x$

The function is defined and continuous on ℝ: there is no vertical asymptote

As $x$ tends to -∞ or to +∞, the function tends to $0$: the line $y=0$ is a horizontal asymptote

▶Asymptotes:   $y=0$

🖼/draw?f1=x%5E3%2F%28x%5E4+%2B+1%29&v=x&f2=0&b=-10.0&e=10.0&min=-0.3951219512195122&max=0.3951219512195122&dash=2