Find the horizontal and vertical asymptote(s) of $LaTeX: \displaystyle f(x) = \frac{x^{2} + 4 x - 165}{4 x^{2} + 4 x - 80}$ , if they exist.

The degree of the numerator is the same as the degree of the denominator, so the horizontal asymptote is the ratio of the leading coefficients $LaTeX: \displaystyle y=\frac{1}{4}$ . The vertical asymptotes are the zeros of the denominator. $LaTeX: \displaystyle 4 x^{2} + 4 x - 80=0 \iff 4 \left(x - 4\right) \left(x + 5\right)=0$ . The vertical asymptotes are $LaTeX: \displaystyle x=-5$ and $LaTeX: \displaystyle x=4$ .