f(x) = 1 / (x + 5) - 9 find horizontal asymptote. x = 9 x = -9 y = 9 y = -9

Explanation:

Step1: Recall horizontal - asymptote rule

For a rational function of the form $y=\frac{f(x)}{g(x)}$ where $f(x)$ and $g(x)$ are polynomials, when the degree of $f(x)$ is less than the degree of $g(x)$, the horizontal asymptote is $y = 0$. For the function $y=\frac{1}{x + 5}-9$, we consider the behavior as $x\to\pm\infty$. As $x\to\pm\infty$, the term $\frac{1}{x + 5}\to0$.

Step2: Find the horizontal asymptote

If $\lim_{x\to\pm\infty}\frac{1}{x + 5}=0$, then $\lim_{x\to\pm\infty}(\frac{1}{x + 5}-9)=0 - 9=-9$.

Answer:

D. $y=-9$