question find all horizontal asymptotes of the following function. f(x) = (3x^2 - 30x)/(x^2 - 4) answer…

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator $n = 2$ (for $3x^{2}-30x$) and the degree of the denominator $m=2$ (for $x^{2}-4$).

Step2: Use the horizontal - asymptote rule for equal degrees

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, $a_{n}=3$ and $b_{m}=1$. So, $y = \frac{3}{1}=3$.

Answer:

$y = 3$