determine all intervals on which $f(x)geq0$.

Explanation:

Step1: Identify x - intercepts

The graph of (y = f(x)) intersects the (x) - axis at (x=-8), (x = - 1), and (x = 6).

Step2: Determine intervals

The intervals to consider are ((-\infty,-8)), ((-8,-1)), ((-1,6)) and ((6,\infty)).

Step3: Check sign of (f(x)) in intervals

• For (x\in(-\infty,-8)), the graph is below the (x) - axis, so (f(x)<0).
• For (x\in(-8,-1)), the graph is above the (x) - axis, so (f(x)>0).
• For (x\in(-1,6)), the graph is above the (x) - axis, so (f(x)>0).
• For (x\in(6,\infty)), the graph is above the (x) - axis, so (f(x)>0).

Answer:

([-8,-1]\cup[-1,6]\cup[6,\infty)=[-8,\infty))