find all horizontal asymptotes of the following function. f(x) = (x^2 - 6x)/(5x^2 - 31x - 28) answer one…

Explanation:

Step1: Identify degrees of polynomials

The degree of the numerator $n = 2$ (for $x^{2}-6x$) and the degree of the denominator $m=2$ (for $5x^{2}-31x - 28$).

Step2: Use 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, $a_{n}=1$ and $b_{m}=5$.

Answer:

$y = \frac{1}{5}$