We have been given a function [tex]f(x)=\text{cos}(8(x-1))+2[/tex]. We are asked to find the amplitude, period and phase shift of the function
We can see that our given function is in form [tex]f(x)=A\cdot \cos(B(x-C))+D[/tex], where,
[tex]|A|[/tex] = Amplitude.
Period = [tex]\frac{2\pi}{|B|}[/tex]
C = Horizontal shift,
D = Vertical shift.
We can see that value of a is 1, therefore, the amplitude of given function would be 1.
We can see that B is equal to 8, so we will get:
[tex]\text{Period}=\frac{2\pi}{|B|}= \frac{2\pi}{|8|}=\frac{\pi}{4}[/tex]
Therefore, the period of given function is [tex]\frac{\pi}{4}[/tex].
Since the value of C is 1, therefore, horizontal shift is 1.
Since the value of D is 2, therefore, vertical shift would be 2.
