What is the range of the function $$G(x) = |x+1|-|x-1|~?$$Express your answer in interval notation.
We have $$G(x) = \begin{cases}
-(x+1)+(x-1) &\text{if }x<-1 \\
(x+1)+(x-1) &\text{if }-1\le x<1 \\
(x+1)-(x-1) &\text{if }x\ge 1
\end{cases}.$$Simplifying, we have $$G(x) = \begin{cases}
-2 &\text{if }x<-1 \\
2x &\text{if }-1\le x<1 \\
2 &\text{if }x\ge 1
\end{cases}.$$Therefore, the range of $G(x)$ is $\boxed{[-2,2]}.$