Question

name the horizontal asymptote(s). $f(x)=\frac{x^{2}+4}{4x^{2}-4x - 8}$

Explanation:

Step1: Identify the degrees of numerator and denominator

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

Step2: Use the horizontal - asymptote rule for equal - degree polynomials

When $n = m$, the horizontal asymptote is $y=\frac{a_{n}}{b_{m}}$, where $a_{n}$ is the leading coefficient of the numerator and $b_{m}$ is the leading coefficient of the denominator. Here, $a_{n}=1$ and $b_{m}=4$. So $y = \frac{1}{4}$.

Answer:

$y=\frac{1}{4}$