find all horizontal asymptotes of the following function.\nf(x)=\frac{x^{2}-8x}{9x^{2}-49}\nanswer attempt 1…

find all horizontal asymptotes of the following function.\nf(x)=\frac{x^{2}-8x}{9x^{2}-49}\nanswer attempt 1 out of 2\none horizontal asymptote

find all horizontal asymptotes of the following function.\nf(x)=\frac{x^{2}-8x}{9x^{2}-49}\nanswer attempt 1 out of 2\none horizontal asymptote

Answer

Explanation:

Step1: Identify degree of polynomials

The degree of the numerator $n = 2$ (for $x^{2}-8x$) and the degree of the denominator $m=2$ (for $9x^{2}-49$).

Step2: Use horizontal - asymptote rule

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 $b_{m}=9$.

Answer:

$y = \frac{1}{9}$