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Answered

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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?


Sagot :

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.

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