https://file.aiquickdraw.com/mathbot/file/17261920896881zswwf26.jpg

The graph shown appears to be a trigonometric function. Let's analyze the graph step by step:

1. **Amplitude**: The maximum and minimum values of the graph are approximately 9 and -9, respectively. Therefore, the amplitude is:
   \[
   \text{Amplitude} = \frac{9 - (-9)}{2} = 9
   \]

2. **Period**: The graph completes one full cycle from approximately -3 to 3. Therefore, the period \( T \) is:
   \[
   T = 3 - (-3) = 6
   \]

3. **Vertical Shift**: The graph is centered around the y-axis with no vertical shift, so the midline is \( y = 0 \).

4. **Form of the Function**: Given the symmetry about the y-axis and the nature of the graph, it appears to be a cosine function:
   \[
   y = A \cos(Bx)
   \]
   where \( A = 9 \) and \( B \) can be calculated using the period formula:
   \[
   \text{Period} = \frac{2\pi}{B} \implies 6 = \frac{2\pi}{B} \implies B = \frac{\pi}{3}
   \]

5. **Equation of the Function**: Substituting these values in, the equation of the function that best describes the graph is:
   \[
   y = 9 \cos\left(\frac{\pi}{3} x\right)
   \]

### Summary
- **Amplitude**: 9
- **Period**: 6
- **Vertical Shift**: 0
- **Equation**: \( y = 9 \cos\left(\frac{\pi}{3} x\right) \)

Would you like more details, or do you have any questions?

### Related Questions
1. What is the phase shift of a trigonometric function, and how can it be calculated?
2. How do you determine whether a function is sine or cosine from its graph?
3. What is the difference between the amplitude and the vertical shift of a function?
4. How do the values of \( A \) and \( B \) in a trigonometric function affect its graph?
5. Can this function be written in terms of sine, and how would that change its equation?

### Tip
Remember that the period of a cosine or sine function is determined by the coefficient \( B \) in front of \( x \) in the general form \( A \cos(Bx) \) or \( A \sin(Bx) \).

What is the equation of the trigonometric function?

Analyze and find the equation of a cosine function with an amplitude of 9 and a period of 6. The graph represents a trigonometric function centered around the y-axis, with no vertical shift. Suitable for high school students learning about trigonometric functions.

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