Question

determine all intervals on which $f(x) \geq 0$.
graph of $f$
answer attempt 2 out of 3

Explanation:

Step1: Identify x-intercepts

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

Step2: Check where $f(x)\geq0$

The graph is above or on the x-axis between $x=-8$ and $x=8$, including the endpoints. The dip at $x=-2$ touches the x-axis ($f(x)=0$), which satisfies $f(x)\geq0$.

Step3: Write the interval

Combine the valid regions into one interval: $[-8, 8]$

Answer:

$[-8, 8]$