I basically sketched the graph. The steps are as follows :
y = 3- 2sin x
First I drew the regular sine graph.
The part in blue represents a vertical stretch of -2. So I multiplied each Y Coordinate by -2
The part in red represents a vertical TRANSLATION of 3 units UPWARDS. So I added 3 to each Y COORDINATE.
You should get a graph as below :
Next, we look at the maximum and minimum Y Value : this is our range for the function.