The function $f(x)$ is defined in three parts:
- For $x < -3$: $f(x) = x + 9$
- For $|x| \leq 3$: $f(x) = -2x$
- For $x > 3$: $f(x) = -6$
Since the function is defined for all real values of $x$, the domain is all real numbers, or $(-\infty, \infty)$.
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