Question

determine all intervals on which $f(x) \geq 0$.

Explanation:

Step1: Identify x-intercepts

The graph crosses/touches the x-axis at $x=-9$, $x=-4$, $x=2$, $x=5$, $x=8$.

Step2: Find regions where $f(x)\geq0$

These are intervals where the graph is on or above the x-axis:

1. From $x=-9$ to $x=-4$: graph is above/on x-axis.
2. From $x=-4$ to $x=2$: graph is above/on x-axis.
3. From $x=5$ to $x=8$: graph is above/on x-axis.

Step3: Write closed intervals

Include endpoints since $f(x)\geq0$ allows $f(x)=0$.

Answer:

$[-9, 2] \cup [5, 8]$