The general form of a cosine function is:
y = A cos (Bx - C) + D
where A is the amplitude, B is the frequency (or 2π divided by the period), C is the phase shift, and D is the vertical shift (or midline).
Using the given information, we can plug in the values to get:
A = 2 (amplitude)
D = 4 (midline)
Period = 1/7
Frequency = 2π / Period = 2π / (1/7) = 14π
So the function is:
y = 2 cos (14πx - C) + 4
where C is the phase shift. Since no phase shift is given, we can assume it to be zero. Therefore, the final equation is:
y = 2 cos (14πx) + 4