Help with graphing a piecewise function

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What would be the graph and domain of this function? My domain is $(- \infty, \infty)$. I am stuck on graphing $-2x$.

$$g(x)=\begin{cases} x+9 & \text{if }x<-3,\\ -2x & \text{if }|x|\leq 3,\\ -6 & \text{if }x>3. \end{cases}$$

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$-2x$ is a straight line. Your domain for this line is $[-3,3]$. At $x=-3$, $-2x=6$. At $x=3,-2x=-6$. So draw a straight line between $(-3,6)$ and $(3,-6)$.