need some help with this one guys..
y=2sin(3x + pi) -1
First of all use the formula $\displaystyle \sin(\pi+x)=-\sin x$.
Then $\displaystyle y=-2\sin 3x-1$
The domain is $\displaystyle \mathbb{R}$.
We have $\displaystyle -1\leq\sin 3x\leq 1\Rightarrow -2\leq -2\sin 3x\leq 2\Rightarrow -3\leq -2\sin 3x-1\leq 1$
So the range is $\displaystyle [-3,1]$