the graph of which function has an amplitude of 3 and a right phase shift of π/4? y = 3sin2(x - π/4) y = 3 +…

Explanation:

Step1: Recall the general form of a sinusoidal function

The general form of a sinusoidal function is $y = A\sin(B(x - C))+D$, where $A$ is the amplitude, $C$ is the phase - shift (positive for right - shift and negative for left - shift), $B$ affects the period ($T=\frac{2\pi}{B}$), and $D$ is the vertical shift.

Step2: Identify the amplitude

We are given that the amplitude $A = 3$. This means the coefficient of the sine function (without considering the argument) should be 3. So we can eliminate the functions $y = 3+\sin2(x-\frac{\pi}{4})$ and $y = 3+\sin2(x + \frac{\pi}{4})$ since their amplitudes are 1 (the coefficient of $\sin$ is 1).

Step3: Identify the phase - shift

We are given that the phase - shift is a right phase - shift of $\frac{\pi}{4}$. In the general form $y = A\sin(B(x - C))+D$, for a right phase - shift of $\frac{\pi}{4}$, we need $C=\frac{\pi}{4}$. The function $y = 3\sin2(x-\frac{\pi}{4})$ has $A = 3$ and a right phase - shift of $\frac{\pi}{4}$, while the function $y = 3\sin2(x+\frac{\pi}{4})$ has a left phase - shift of $\frac{\pi}{4}$.

Answer:

$y = 3\sin2(x-\frac{\pi}{4})$