Answer
$(1,3]$ and Range: $[-\pi,0]$
Work Step by Step
A phase shift of $2$ results in shifting the domain of the sine curve right by $2$ and a vertical shift of $-\dfrac{\pi}{2}$ results in shifting the range of the curve down by an angle of $\dfrac{\pi}{2}$.
Therefore, we have the Domain and Range of the function as follows:
Domain : $(1,3]$ and Range: $[-\pi,0]$
