Question

Determine the amplitude (A), period (P), and phase shift (PS) of the function f(x)= 3sin(x-4)+9

Answer 1

ANSWER

D.

`A=3,P=2\pi,PS=(4,9)`

Step-by-step explanation

The given function is


`f(x) = 3 \sin(x - 4) + 9`

Comparing to the general form of a trigonometric sine function,


`f(x) = A \sin(Bx-C)+D`


`A=3`
The amplitude is absolute value of A


`|A| = |3| = 3`


`B=1`

The period is given by


`p = (2\pi)/( B)`


`p = (2\pi)/( 1) = 2\pi`


`C=4`

is a shift to the right of 4 units.

and


`D=9`

is an upward shift of 9 units

Therefore the phase shift is (4,9).

The correct answer is D