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

the graph of which function has an amplitude of 3 and a right phase shift of $\frac{pi}{4}$?\n$y = 3sin2(x+\frac{pi}{4})$ $y = 3+sin2(x+\frac{pi}{4})$ $y = 3sin2(x - \frac{pi}{4})$ $y = 3+sin2(x - \frac{pi}{4})$

the graph of which function has an amplitude of 3 and a right phase shift of $\frac{pi}{4}$?\n$y = 3sin2(x+\frac{pi}{4})$ $y = 3+sin2(x+\frac{pi}{4})$ $y = 3sin2(x - \frac{pi}{4})$ $y = 3+sin2(x - \frac{pi}{4})$

Answer

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 $C$ means right - shift), $B$ affects the period ($T=\frac{2\pi}{B}$), and $D$ is the vertical shift.

Step2: Identify the amplitude and phase - shift requirements

We are given that the amplitude $A = 3$ and the right phase - shift $C=\frac{\pi}{4}$.

Step3: Analyze each option

  • For $y = 3\sin2(x+\frac{\pi}{4})$, the phase - shift is $-\frac{\pi}{4}$ (left - shift), so it is incorrect.
  • For $y = 3+\sin2(x+\frac{\pi}{4})$, the amplitude is $1$ and the phase - shift is $-\frac{\pi}{4}$ (left - shift), so it is incorrect.
  • For $y = 3\sin2(x - \frac{\pi}{4})$, the amplitude $A = 3$ and the phase - shift $C=\frac{\pi}{4}$ (right - shift), which meets the requirements.
  • For $y = 3+\sin2(x - \frac{\pi}{4})$, the amplitude is $1$, so it is incorrect.

Answer:

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