Answer:
B) As x --->∞, f(x) = -∞ and as x --->-∞, f(x) --->-∞
Step-by-step explanation:
Given function f(x) = -x^3 (x - 9)^3 (x + 5)
First let's see how the function behave when x --> ∞,
When we plug in x = ∞, we get
f(∞) = -∞^3 (∞ - 9)^3 (∞ + 5)
= -∞(∞)(∞) [Because ∞ is assume a biggest number, so we have to see
sign alone]
= -∞
So when x -->∞, f(x) -->-∞
Now we have to see how the function behave when x -->-∞
When we plug in x = -∞, we get
f(-∞) = - (-∞)^3 (-∞ - 9)^3 (-∞ + 5)
= -(-∞)(-∞)(-∞) [Because odd power of negative number get negative]
= -∞ [By sign rule]
when x-->-∞, we get f(x) -->-∞
Therefore, the answer is B) As x --->∞, f(x) = -∞ and as x --->-∞, f(x) --->-∞
Hope this will helpful.
Thank you.
