Match each function in Column I with the appropriate description in Column II.

I
y = 3 sin(2x - 4)

II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

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Identify the general form of the sine function: \(y = A \sin(Bx - C)\), where \(A\) is the amplitude, \(B\) affects the period, and \(C\) affects the phase shift.

From the given function \(y = 3 \sin(2x - 4)\), note that the amplitude \(A\) is the coefficient before the sine, which is 3.

Calculate the period using the formula \(\text{Period} = \frac{2\pi}{B}\). Here, \(B = 2\), so the period is \(\frac{2\pi}{2} = \pi\).

Find the phase shift using the formula \(\text{Phase shift} = \frac{C}{B}\). Since the function is \(\sin(2x - 4)\), rewrite the inside as \(2(x - 2)\), so the phase shift is \(\frac{4}{2} = 2\).

Match the values amplitude = 3, period = \(\pi\), and phase shift = 2 with the correct description in Column II, which corresponds to option B.

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