Consider the function $f(x) = \frac{4x^2 + 25x}{x^2 + 5x}$
(a) Evaluate $\lim_{x \to \infty} f(x)$ and $\lim_{x \to -\infty} f(x)$, then identify the horizontal asymptotes.
(b) Find the vertical asymptote. For the vertical asymptote $x=a$, evaluate $\lim_{x \to a^-} f(x)$ and $\lim_{x \to a^+} f(x)$.
$\lim_{x \to \infty} f(x) = 4$
$\lim_{x \to -\infty} f(x) = 4$
Identify the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The horizontal asymptote(s) is/are $y = 4$.
(Use a comma to separate answers as needed.)
B. There are no horizontal asymptotes.
(b) Find the vertical asymptote. For the vertical asymptote $x=a$, evaluate $\lim_{x \to a^-} f(x)$ and $\lim_{x \to a^+} f(x)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The vertical asymptote is $x = -5$. The limits at this vertical asymptote are $\lim_{x \to a^-} f(x) = \infty$ and $\lim_{x \to a^+} f(x) = -\infty$.
B. There is no vertical asymptote.
