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The graph you've provided shows a periodic function, which appears sinusoidal in nature. Let's break down its key characteristics:

### Observations:
1. **Amplitude**: The function oscillates between a maximum value of 3 and a minimum value (which looks like -3). So, the amplitude \( A \) is 3.
2. **Period**: The function completes one full cycle over the horizontal length of \( 14\pi \). Therefore, the period \( T \) is \( 14\pi \).
3. **Vertical Shift**: There is no vertical shift since the function seems centered around the x-axis.
4. **Phase Shift**: Based on the graph, the function starts at its maximum value, indicating there is no phase shift.

### General Form:
The general formula for a sinusoidal function is:

\[
f(x) = A \sin(Bx + C) + D
\]

Where:
- \( A \) is the amplitude (3 here).
- \( B \) is related to the period by the formula \( B = \frac{2\pi}{T} \).
- \( C \) represents the phase shift (0 here).
- \( D \) represents the vertical shift (0 here).

### Calculating \( B \):
Since the period \( T \) is \( 14\pi \), we can calculate \( B \):

\[
B = \frac{2\pi}{14\pi} = \frac{1}{7}
\]

Thus, the equation becomes:

\[
f(x) = 3 \sin\left(\frac{1}{7}x\right)
\]

### Considering Cosine:
Since the graph starts at its maximum value (which is typical for a cosine function), a cosine function might be a more appropriate choice. The cosine function reaches its maximum at \( x = 0 \), which matches the graph.

Thus, the formula becomes:

\[
f(x) = 3 \cos\left(\frac{1}{7}x\right)
\]

### Final Answer:
A possible formula for the function is:

\[
f(x) = 3 \cos\left(\frac{1}{7}x\right)
\]

Would you like further clarification or additional details on this solution?

Here are some related questions to deepen your understanding:
1. How does the amplitude affect the shape of a sinusoidal graph?
2. What is the relationship between the period and the value of \( B \) in a sinusoidal function?
3. How can we determine if a sinusoidal graph should be modeled by a sine or cosine function?
4. What changes in the formula if the function has a phase shift?
5. How does a vertical shift affect the equation of a trigonometric function?

**Tip:** When modeling periodic functions, always check the key parameters: amplitude, period, phase shift, and vertical shift.

Find a possible formula for the function graphed below.

Learn how to find a possible formula for a trigonometric function based on a graph showing amplitude and period. This problem covers key concepts like amplitude, period, and phase shift in trigonometric functions, and how to derive the function's formula using sine or cosine.

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