find all horizontal asymptotes of the following function.\nf(x)=\frac{3x - 27}{5x^{2}-52x + 63}

Explanation:

Step1: Recall the rule for horizontal asymptotes

To find horizontal asymptotes of a rational function $\frac{f(x)}{g(x)}$ where $f(x)=3x - 27$ and $g(x)=5x^{2}-52x + 63$, we consider the degrees of the numerator and denominator polynomials.

Step2: Compare the degrees

The degree of the numerator $n = 1$ (since the highest - power of $x$ in $3x-27$ is 1) and the degree of the denominator $m = 2$ (since the highest - power of $x$ in $5x^{2}-52x + 63$ is 2). When $n<m$, the horizontal asymptote is $y = 0$.

Answer:

$y = 0$