Question

Select the correct answer.
Which statement describes the end behavior of the function?
f(x)= x squared-4/x squared-9

ОА.
The function approaches O as x approaches - and co.
OB.The function approaches 4/5 as x approaches -- and co.
OC. The function approaches 2/3 as x approaches - and co.
OD. The function approaches 1 as x approaches -co and co.

Answer 1

Answer:

D. The function approaches 1 as x approaches $-\infty$ and $\infty$

Step-by-step explanation:

When evaluating end behavior, take the limit as the function goes to negative and positive infinity.

When evaluating limits to infinity, terms less than the highest degree are irrelevant:

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

Therefore, the function approaches 1 as x approaches $-\infty$ and $\infty$