# What is the horizontal asymptote of the graph of y=(3x^6-7x+10)/(8x^5+9x+10)?

If you evaluate the limits at $\infty$ you get:
${\lim}_{x \to \infty} f \left(x\right) = \infty$ and
${\lim}_{x \to - \infty} f \left(x\right) = - \infty$
The graph does not pass through the origin (when $x = 0 , y = 1$), and near the origin you have: