Question

consider the following equation:
$f(x)=\frac{x^2 + 4}{4x^2 - 4x - 8}$
name the vertical asymptote(s).
$\boldsymbol{\checkmark x = -1}$ and $\boldsymbol{x = 2 \checkmark}$
complete
name the horizontal asymptote(s).
done $\boldsymbol{\checkmark}$
because
$\circ$ $m < n$
$\circ$ $m = n$
$\circ$ $a_m < b_n$
$\circ$ $a_m = b_n$
$\boldsymbol{\checkmark}$ this is where the function is undefined

Explanation:

Step1: Identify degrees of numerator/denominator

For $f(x)=\frac{x^2 + 4}{4x^2 - 4x - 8}$, degree of numerator $m=2$, degree of denominator $n=2$, so $m=n$.

Step2: Find horizontal asymptote

When $m=n$, horizontal asymptote is $y=\frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}} = \frac{1}{4}$.

Answer:

Horizontal asymptote: $y=\frac{1}{4}$
Reason: $m = n$