Write a cosine function that has a midline of 2, an amplitude of 4 and a period of
8/3

f(x) = 4*cos(pi*(6/8)*x) + 2

Step-by-step explanation:

A generic cosine function is written as:

f(x) = A*cos(w*x + p) + M

where:

A = amplitude

w = angular frequency

p = phase

M = midline.

We know that:

the midline is 2, then  M = 2

the amplitude is 4, then A  = 4

There is no information about the phase, so p = 0.

And we know that the period is 8/3.

The period is written as T, and the relation between the period and the angular frequency is:

T = 2*pi/w

Then we have:

8/3 = 2*pi/w

w = (2*pi)*(3/8) = pi*(6/8)

where pi = 3.14

Then we have:

w =  pi*(6/8)

A = 4

M = 2

p = 0

Then the cosine function is:

f(x) = 4*cos(pi*(6/8)*x) + 2.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.