Answer:
The correct option is 4. Amplitude: 3; midline: y = 2
Step-by-step explanation:
The graph passing through the points (0,2), [tex](\frac{\pi}{2},5),(\pi,2),(\frac{3\pi}{2},-1),(2\pi,2)[/tex].
If a is maximum value and b is minimum value, then
[tex]Amplitude=\frac{a-b}{2}[/tex]
[tex]Midline=\frac{a+b}{2}[/tex]
The minimum value of the function is -1.
The maximum value of the function is 5.
[tex]Amplitude=\frac{5-(-1)}{2}=\frac{6}{2}=3[/tex]
The amplitude of the graph is 3.
[tex]Midline=\frac{5+(-1)}{2}=\frac{4}{2}=2[/tex]
The midline of the graph is y=2.
The general sine function is
[tex]f(x)=A\sin (Bx+C)+D[/tex]
Where, A is amplitude, 2π/B is period, C is phase shift and D is midline.
The required function is
[tex]f(x)=3\sin x+2[/tex]
Therefore correct option is 4.
