We have the form
y = Acos (Bx +C) + D
A = amplitude = [ high point - low point ] / 2 = [ 3 - - 11 ] / 2 = 14 / 2 = 7
D = the vertical shift = [ hight point + low pont ] / 2 = [ 3 -11] / 2 = -8 / 2 = -4
The period = 9pi/4 - pi/4 = 8pi/4 = 2pi
B = 2pi/ period = 2pi / [2pi] = 1
C = the phase shift = pi/4 units to the right
So.....the function is
y = 7cos ( x - pi/4) - 4