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
(type an equation.)
b. there is no vertical asymptote.

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0.
$x + 2=0$

Step2: Solve for x

$x=-2$

Step3: Check degree of numerator and denominator for horizontal/oblique asymptote

Degree of numerator ($n = 2$) is greater than degree of denominator ($m = 1$), so there is no horizontal asymptote. Since $n=m + 1$, there is an oblique asymptote. We can find it by long - division of polynomials: $\frac{4x^{2}+1}{x + 2}=4x-8+\frac{17}{x + 2}$. The oblique asymptote is $y = 4x-8$. But we are only asked for vertical asymptote here.

Answer:

A. The equation of the vertical asymptote is $x=-2$