the graph of which function has an amplitude of 3 and a right phase shift of $\frac{pi}{4}$?\n$y = 3sin…

the graph of which function has an amplitude of 3 and a right phase shift of $\frac{pi}{4}$?\n$y = 3sin 2(x+\frac{pi}{4})$ $y = 3+sin 2(x+\frac{pi}{4})$ $y = 3+sin 2(x - \frac{pi}{4})$ $y = 3sin 2(x - \frac{pi}{4})$

the graph of which function has an amplitude of 3 and a right phase shift of $\frac{pi}{4}$?\n$y = 3sin 2(x+\frac{pi}{4})$ $y = 3+sin 2(x+\frac{pi}{4})$ $y = 3+sin 2(x - \frac{pi}{4})$ $y = 3sin 2(x - \frac{pi}{4})$

Answer

Explanation:

Step1: Recall amplitude - phase shift formula

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).

Step2: Identify amplitude

We are given that the amplitude $A = 3$. So the function should be of the form $y=3\sin(B(x - C))+D$. This eliminates the functions $y = 3+\sin2(x+\frac{\pi}{4})$ and $y = 3+\sin2(x - \frac{\pi}{4})$ since their amplitudes are 1.

Step3: Identify phase - shift

We are given that the right phase - shift is $\frac{\pi}{4}$, so $C=\frac{\pi}{4}$. The function should be of the form $y = 3\sin(B(x-\frac{\pi}{4}))+D$.

Answer:

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