In the function y=sin(b(x+c))+d, the two parameters that will influence the range are a and d, which are the amplitude and vertical transformation, respectively.
The function y=sinx has an amplitude of 1 and a vertical transformation of 0, for example. Since the sine function rotates around the centre line which will be at y=0 (due to the vertical transformation), the range will be −1≤y≤1.
With our function, the amplitude is |−2|=2 and the vertical transformation brings the centre line down to y=−3. Hence, the minimum values will be y=−3−2=−5 and our maximum values will be y=−3+2=−1.
The range is therefore −5≤y≤−1.
Hopefully this helps!
