Question

determine all intervals on which the graph of f is decreasing.

Explanation:

Step1: Recall the concept of a decreasing function

A function $y = f(x)$ is decreasing on an interval if, for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$. On a graph, the function is decreasing when it is moving down - ward as we move from left to right.

Step2: Analyze the given graph

Looking at the graph of $y = f(x)$, we can see that the graph is moving downward from $x=-8$ to $x = - 3$. Also, the graph is moving downward from $x = 1$ to $x=3$.

Answer:

$(-8,-3)\cup(1,3)$