Question

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 1

The required function is f(x)=4sinx-1.

Explanation:

The standard sine function is defined as

`f(x)=a\sin(b(x+c))+d` ....(1)

Where a is amplitude, period is
`(2\pi )/(b)`, 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.

`a=(3-(-5))/(2)=4`

The value of a is 4.

The period is 2π.

`(2\pi)/(b)=2\pi`

`b=1`

Midline is average of maximum and minimum.

`d=(3-5)/(2)=-1`

Substitute a=4, b=1, c=0 and d=1 in equation (1).

`f(x)=4\sin(x)-1`

Therefore the required function is f(x)=4sinx-1.