Which of the following is the graph of y = 45inx? %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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How can you graph this please
**Question:**

Which of the following is the graph of \( y = 4 \sin \left( \frac{\pi}{4} x \right) \)?

**Graph Description:**

The graph shown is a sinusoidal wave representing the function \( y = 4 \sin \left( \frac{\pi}{4} x \right) \).

- **Amplitude:** The maximum and minimum values are \( 4 \) and \(-4\), respectively, indicating an amplitude of \( 4 \).
- **Period:** The period of the sine function is determined by the coefficient of \( x \) inside the sine function. Here, the period is \( \frac{2\pi}{\frac{\pi}{4}} = 8 \).
- **X-Intercepts:** The graph crosses the x-axis at \( x = 0, 4, 8, \ldots \).
- **Y-Intercept:** The graph starts at \( (0,0) \), since \( \sin(0) = 0 \).
- **Behavior:** The wave rises to \( 4 \) at \( x = 2 \) and falls back to \( 0 \) at \( x = 4 \), then continues symmetrically.

The sinusoidal pattern repeats every 8 units along the x-axis.
Transcribed Image Text:**Question:** Which of the following is the graph of \( y = 4 \sin \left( \frac{\pi}{4} x \right) \)? **Graph Description:** The graph shown is a sinusoidal wave representing the function \( y = 4 \sin \left( \frac{\pi}{4} x \right) \). - **Amplitude:** The maximum and minimum values are \( 4 \) and \(-4\), respectively, indicating an amplitude of \( 4 \). - **Period:** The period of the sine function is determined by the coefficient of \( x \) inside the sine function. Here, the period is \( \frac{2\pi}{\frac{\pi}{4}} = 8 \). - **X-Intercepts:** The graph crosses the x-axis at \( x = 0, 4, 8, \ldots \). - **Y-Intercept:** The graph starts at \( (0,0) \), since \( \sin(0) = 0 \). - **Behavior:** The wave rises to \( 4 \) at \( x = 2 \) and falls back to \( 0 \) at \( x = 4 \), then continues symmetrically. The sinusoidal pattern repeats every 8 units along the x-axis.
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