question find all horizontal asymptotes of the following function. f(x) = (3x² - 10x - 8)/(3x² - 36x + 96)…

question find all horizontal asymptotes of the following function. f(x) = (3x² - 10x - 8)/(3x² - 36x + 96) answer one horizontal asymptote submit answer

question find all horizontal asymptotes of the following function. f(x) = (3x² - 10x - 8)/(3x² - 36x + 96) answer one horizontal asymptote submit answer

Answer

Answer:

$y = 1$

Explanation:

Step1: Identify degree of numerator and denominator

Degree of numerator $n = 2$, degree of denominator $m = 2$.

Step2: Recall horizontal - asymptote rule

When $n=m$, horizontal asymptote is $y=\frac{a_n}{b_m}$, where $a_n$ and $b_m$ are leading coefficients.

Step3: Find leading coefficients

Leading coefficient of numerator $a_n = 3$, leading coefficient of denominator $b_m = 3$.

Step4: Calculate horizontal asymptote

$y=\frac{3}{3}=1$.