Answer
The line $ y=0$ is the horizontal asymptote of the given function.
Work Step by Step
To find the horizontal asymptotes, we calculate the following limit
\begin{align*}
\lim _{x \rightarrow \pm \infty}\frac{8x^3-x^2}{7+11x-4 x^4}&= \lim _{x \rightarrow \pm\infty} \frac{x^3}{x^4}\frac{8 -x^{-1}}{7x^{-1}+11x^{-3}-4 }\\
&=\frac{8}{-4} \lim _{x \rightarrow \pm\infty} \frac{x^3}{x^4}\\
&=\frac{8}{-4} \lim _{x \rightarrow \pm\infty} x^{-1}\\
&=0.\\
\end{align*}
Hence, the line $ y=0$ is the horizontal asymptote of the given function.
