1. The problem asks us to determine over which intervals the function $f$ is increasing based on its graph. 2. A function is increasing on an interval if, as $x$ moves from left to right within that interval, the function values $f(x)$ go up (i.e., $f(x)$ increases). 3. From the graph points given: $(-6, -3)$, $(-4, 3)$, $(0, 3)$, $(2, -4)$, and $(5, 3)$, we analyze the slope between these points. 4. Between $x=-6$ and $x=-4$, $f$ goes from $-3$ to $3$, which is an increase. 5. Between $x=-4$ and $x=0$, $f$ stays constant at $3$, so it is not increasing. 6. Between $x=0$ and $x=2$, $f$ decreases from $3$ to $-4$. 7. Between $x=2$ and $x=5$, $f$ increases from $-4$ to $3$. 8. Therefore, $f$ is increasing on the intervals $[-6, -4]$ and $[2, 5]$. 9. The correct answer is option A: $[-6, -4]$ and $[2, 5]$.