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The graph of which function has an amplitude of 3 and a right phase shift of π/4?

A: y= 3sin2(x- π/4)

B: y = 3 + sin2(x- π/4)

C:y = 3 + sin2(x+ π/4)

D:y = 3sin2(x+π/4)​

Respuesta :

MrRoyal

Answer:

[tex]D.\ y = 3\sin(2(x + \frac{\pi}{4}))[/tex]

Step-by-step explanation:

Given

[tex]A = 3[/tex] --- Amplitude

[tex]C = \frac{\pi}{4}[/tex] --- Right phase shift

Required

Identify the function

A sinusoidal function is defined as:

[tex]y = A\sin(B(x + C)) + D[/tex]

Substitute values for A and C

[tex]y = 3\sin(B(x + \frac{\pi}{4})) + D[/tex]

By comparison, only option (D) has the above format where

[tex]y = 3\sin(2(x + \frac{\pi}{4}))[/tex]

Hence (D) is correct

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