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!
