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

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

  • $\begingroup$ -2x is a linear function, just take two points,draw a line between those points, and extrapolate $\endgroup$ – chubakueno Jul 2 '13 at 2:38
  • $\begingroup$ You are probably intending to ask about the range, not the domain. $\endgroup$ – André Nicolas Jul 2 '13 at 2:42
  • $\begingroup$ @chubakueno will it be overlapping -6? $\endgroup$ – eLg Jul 2 '13 at 2:43
  • $\begingroup$ @AndréNicolas its asking for the domain. Anyways, will the range be (- ∞, ∞)? what will I do if the domain is somthing like the domain of -2x? $\endgroup$ – eLg Jul 2 '13 at 2:45
  • $\begingroup$ The domain, as you say in your post, is all reals. $\endgroup$ – André Nicolas Jul 2 '13 at 2:46

$-2x$ 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 $(3,-6)$.


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