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