Micah
has been following stock ratings. He is keeping his eye on Sam's Pork
Bellies, and the pattern can be modeled by a sine function. He has found
it to have a maximum of 3, minimum of −5, and period of 2π. Which of
the following sine functions could model Micah's stock rating?

Answer:The required function is f(x)=4sinx-1.Step-by-step explanation:The standard sine function is defined as[tex]f(x)=a\sin(b(x+c))+d[/tex]                    ....(1)Where a is amplitude, period is [tex]\frac{2\pi }{b}[/tex], c is phase shift and d is midline.It is given that the maximum value is 3 and the minimum value is -5. Amplitude is half of difference between minimum and maximum.[tex]a=\frac{3-(-5)}{2}=4[/tex]The value of a is 4.The period is 2π.[tex]\frac{2\pi}{b}=2\pi[/tex][tex]b=1[/tex]Midline is average of maximum and minimum.[tex]d=\frac{3-5}{2}=-1[/tex]Substitute a=4, b=1, c=0 and d=1 in equation (1).[tex]f(x)=4\sin(x)-1[/tex] Therefore the required function is f(x)=4sinx-1.