Question

give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function.
f(x) = \frac{4x^{2}+1}{x + 2}
select the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. the equation of the vertical asymptote is x = - 2.
(type an equation.)
b. there is no vertical asymptote.
select the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. the equation of the horizontal asymptote is
(type an equation.)
b. there is no horizontal asymptote.

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. For $f(x)=\frac{4x^{2}+1}{x + 2}$, we solve $x+2=0$, getting $x=-2$.

Step2: Find horizontal asymptote

Degree of numerator ($n = 2$) is greater than degree of denominator ($m=1$). So, there is no horizontal asymptote.

Answer:

A. The equation of the vertical asymptote is $x=-2$.
B. There is no horizontal asymptote.