ANSWER
D.
[tex] A=3,P=2\pi,PS=(4,9)[/tex]
EXPLANATION
The given function is
[tex]f(x) = 3 \sin(x - 4) + 9[/tex]
Comparing to the general form of a trigonometric sine function,
[tex]f(x) = A \sin(Bx-C)+D[/tex]
[tex]A=3[/tex]
The amplitude is absolute value of A
[tex] |A| = |3| = 3[/tex]
[tex]B=1[/tex]
The period is given by
[tex]p = \frac{2\pi}{ B} [/tex]
[tex]p = \frac{2\pi}{ 1} = 2\pi[/tex]
[tex]C=4[/tex]
is a shift to the right of 4 units.
and
[tex]D=9[/tex]
is an upward shift of 9 units
Therefore the phase shift is (4,9).
The correct answer is D
