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
Answer:
$y = \frac{1}{4}$
Explanation:
Step1: Check 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 given by $y=\frac{a_{n}}{b_{m}}$, where $a_{n}$ is the leading coefficient of the numerator and $b_{m}$ is the leading coefficient of the denominator.
Step3: Identify leading coefficients
The leading coefficient of the numerator $a_{n}=1$ (from $x^{2}$) and the leading coefficient of the denominator $b_{m}=4$ (from $4x^{2}$).
Step4: Calculate the horizontal asymptote
$y=\frac{1}{4}$.