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The question asks for the graph of \( y = 2 \sin(3x) \).

### Key properties of the function \( y = 2 \sin(3x) \):
1. **Amplitude**: The coefficient of the sine function is 2, meaning the amplitude is 2. This indicates that the graph will oscillate between -2 and 2 on the y-axis.
   
2. **Period**: The period of a sine function is given by \( \frac{2\pi}{B} \), where \( B \) is the coefficient of \( x \) inside the sine. In this case, \( B = 3 \), so the period is:
   \[
   \text{Period} = \frac{2\pi}{3}
   \]
   This means the sine wave will complete one full cycle every \( \frac{2\pi}{3} \) units along the x-axis.

3. **Frequency**: Since the sine function repeats every \( \frac{2\pi}{3} \), it will have a higher frequency than the regular sine function.

### Identifying the correct graph:
- The amplitude is 2, so the graph should have peaks at 2 and valleys at -2.
- The period is \( \frac{2\pi}{3} \), so the graph should complete one cycle in that span.

The second graph from the left matches these properties, as it has the correct amplitude of 2 and period of \( \frac{2\pi}{3} \).

**Answer: The correct graph is the second one from the left.**

Would you like more details on any of these points? 

### Here are five related questions you might find helpful:
1. How do you determine the amplitude of a sine function from its equation?
2. What is the relationship between the coefficient of \( x \) inside the sine function and the period?
3. How do transformations (like vertical shifts) affect the graph of a sine function?
4. What would the graph look like if the equation was \( y = 2 \cos(3x) \)?
5. How does the frequency of a sine wave change when you change the coefficient of \( x \)?

### Tip:
When identifying graphs of sine or cosine functions, always start by analyzing the amplitude and period, as these will give you the key characteristics to look for.

Which of the following is the graph of y = 2 sin(3x)?

Learn how to graph the sine function y = 2sin(3x). This example demonstrates how to find the amplitude and period of the function, and how these properties affect the graph. Suitable for students in Grades 10-12.

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