How to use graph to determine where f(x) > 0 and f(x) < 0

Question

How to write this in interval notation? I can't seem to get the right answer.

Answer 1

Notice that the graph of $f$ crosses the $x$-axis at $-3,-2,0,2$ and $3$. Using the fact $f(x)>0$ on the interval where the graph is above the $x$-axis, and $f(x)<0$ on the interval where the graph is below the $x$-axis we have:

a. $f(x)>0$ for $x\in (-3,-2)\cup(0,2)\cup(3,\infty)$

b. $f(x)<0$ for $x\in (-\infty,-3)\cup(-2,0)\cup(2,3)$

Answer 2

Find where it crosses 0. Use open intervals in between. Ex (3, $\infty$)