To determine the horizontal asymptote(s) of a rational function, we need to analyze the behavior of the function as $x \to \infty$ or $x \to -\infty$. The general form of a rational function is:

$f(x) = \frac{P(x)}{Q(x)}$

where $P(x)$ and $Q(x)$ are polynomials.

Steps to determine horizontal asymptotes:

1. Degree of the numerator ( $P(x)$ ) and denominator ( $Q(x)$ ):
   • If the degree of $P(x)$ is less than the degree of $Q(x)$, the horizontal asymptote is $y = 0$.
   • If the degree of $P(x)$ equals the degree of $Q(x)$, the horizontal asymptote is $y = \frac{\text{leading coefficient of } P(x)}{\text{leading coefficient of } Q(x)}$.
   • If the degree of $P(x)$ is greater than the degree of $Q(x)$, there is no horizontal asymptote.

If you have a specific function in mind, feel free to share it with me so I can help determine the horizontal asymptote(s) more precisely.