f(x)=\frac{x^{2}+4}{4x^{2}-4x - 8}\nname the horizontal asymptote(s).
f(x)=\frac{x^{2}+4}{4x^{2}-4x - 8}\nname the horizontal asymptote(s).
Answer
Explanation:
Step1: Determine degrees of polynomials
The degree of the numerator $n = 2$ (for $x^{2}+4$) and the degree of the denominator $m = 2$ (for $4x^{2}-4x - 8$).
Step2: Find the horizontal - asymptote formula
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 $b_{m}=4$.
Answer:
$y = \frac{1}{4}$