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

Question

asked Mar 28, 2021 87.3k views

1 Answer

Mirosval · Answer 1 · 2021-04-01T05:14:10+0000

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 =
$(2\pi)/(|B|)$

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:

$\text{Period}=(2\pi)/(|B|)= (2\pi)/(|8|)=(\pi)/(4)$

Therefore, the period of given function is
$(\pi)/(4)$ .

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.