Answer: The correct option is 1.
Explanation:
The from the given graph it is noticed that the function must be in he form of,
[tex]y=asin(bx+c)+d[/tex]
Where, a is amplitude, b is period, c is horizontal shift and d is vertical shift.
From the given figure it is noticed that the graph has period of [tex]\pi[/tex], it means the value of b is 2. The value of amplitude must be negative, because the graph of sine is reflected along the y axis.
The option 2 has period of [tex]2\pi[/tex], therefore it is not the correct option. The option 4 has period of [tex]\frac{\pi}{2}[/tex], therefore it is not the correct option.
The option 4 has positive amplitude, therefore it is not the correct option.
Thus, the correct option is 1 and the function of the graph is [tex]y=-3\sin (2(x+\pi))+2[/tex].
