Question

WILL GIVE BRAINLIEST AND 33 POINTS!! Determine the end behavior of the function.

Answer 1

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.