Question

Determine the amplitude, period, and phase shift of the function f(x)=cos (8(x-1))+2​

Answer 1

We have been given a function $f(x)=\text{cos}(8(x-1))+2$. We are asked to find the amplitude, period and phase shift of the function

We can see that our given function is in form $f(x)=A\cdot \cos(B(x-C))+D$, where,

$|A|$ = Amplitude.

Period = $\frac{2\pi}{|B|}$

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:

$\text{Period}=\frac{2\pi}{|B|}= \frac{2\pi}{|8|}=\frac{\pi}{4}$

Therefore, the period of given function is $\frac{\pi}{4}$.

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.