Question

use interval notation to describe where f is increasing and where f is decreasing (please lable your answers as increasing or decreasing)

Answer 1

In order to determine the intervals in which the function is increasing or decreasing, you take into account that can be considered, that a function increases until a point in which the value of the function for a consecutive point is not higher than the previous one.

So, what you have is that the given function is increasing from -infinity to the point x=-3. Next, the function decreases to the point x = 0. Next, function increases to point x = 3, and finally decreases from x = 3 to = infinity.

Summarizing, you have:

(-∞ , -3) increases

(-3 , 0 ) decreases

(0 , 3) increases

(3 , +∞) decreases