Let's break down the graph of the piecewise function to fill in the missing intervals:

Observations:

1. For $f(x) = 3$:

   • From the graph, we see a horizontal line at $y = 3$ between $x = -6$ and $x = -3$. Both endpoints are closed, so this segment is included in the domain.
   • Therefore, $f(x) = 3$ for $-6 \leq x \leq -3$.

2. For $f(x) = -2$:

   • There is a horizontal line at $y = -2$ between $x = -2$ and $x = 1$, with an open circle at $x = -2$ and a closed circle at $x = 1$. So, $x = -2$ is excluded, but $x = 1$ is included.
   • Hence, $f(x) = -2$ for $-2 < x \leq 1$.

3. For $f(x) = -5$:

   • A horizontal line at $y = -5$ exists between $x = 2$ and $x = 6$, with open circles at both $x = 2$ and $x = 6$. So both endpoints are excluded.
   • Therefore, $f(x) = -5$ for $2 < x < 6$.

Completed Piecewise Function: