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The problem asks for the graph of the function \( y = \sin\left(\frac{1}{11}x\right) \), and it also asks for the period of the function.

### Step-by-Step Solution:

1. **General Sine Function Form:**
   The standard sine function is \( y = \sin(bx) \), where the period is given by:
   \[
   \text{Period} = \frac{2\pi}{b}
   \]
   In this case, \( b = \frac{1}{11} \).

2. **Calculate the Period:**
   The period is:
   \[
   \text{Period} = \frac{2\pi}{\frac{1}{11}} = 2\pi \times 11 = 22\pi
   \]
   Therefore, the period of the function is \( 22\pi \).

3. **Correct Graph:**
   The graph of \( y = \sin\left(\frac{1}{11}x\right) \) should show a sine wave that completes one cycle over an interval of \( 22\pi \) on the x-axis.

4. **Examine the Options:**
   The graph must stretch over a long interval because the period is large. From the available options:
   - Option **A** and **C** have periods that are too short.
   - Option **B** correctly shows a wave that repeats over a large interval, matching the calculated period.
   - Option **D** has a period that is also too short.

Thus, the correct answer is **B**.

### Would you like further explanation or details about the period and graph of sine functions? 

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### Related Questions:
1. What happens to the period when the coefficient \( b \) increases in \( y = \sin(bx) \)?
2. How would the graph change if the function was \( y = \sin\left(\frac{1}{5}x\right) \)?
3. How do amplitude and phase shift affect the graph of sine functions?
4. What is the relationship between the frequency and the period of a sine wave?
5. How can we determine the phase shift in a function like \( y = \sin\left(\frac{1}{11}(x - \pi)\right) \)?

### Tip:
The period of any sine function is inversely proportional to the coefficient of \( x \) inside the sine, so a smaller coefficient results in a longer period.

Graph the following function over a two-period interval: y = sin(1/11 * x). Identify the correct graph from the options.

Learn how to graph the sine function y = sin(1/11 * x) and understand its period calculation. This trigonometry problem is suitable for students in Grades 10-12, and it focuses on identifying the correct graph over a two-period interval.

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