describe the end behavior of f(x)=(x² - 9)/(x² - 4) as x approaches negative infinity? 9/4 f(x)→9/4 1 f(x)→1…

Explanation:

Step1: Divide numerator and denominator by $x^{2}$

$\lim_{x\rightarrow-\infty}\frac{x^{2}-9}{x^{2}-4}=\lim_{x\rightarrow-\infty}\frac{1 - \frac{9}{x^{2}}}{1-\frac{4}{x^{2}}}$

Step2: Evaluate the limit as $x\rightarrow-\infty$

As $x\rightarrow-\infty$, $\frac{9}{x^{2}}\rightarrow0$ and $\frac{4}{x^{2}}\rightarrow0$. So $\lim_{x\rightarrow-\infty}\frac{1 - \frac{9}{x^{2}}}{1-\frac{4}{x^{2}}}=\frac{1 - 0}{1-0}=1$

Answer:

D. $f(x)\rightarrow1$