https://file.aiquickdraw.com/mathbot/file/17264107399303v1lk8rx.jpg

The graph shown in the image resembles a transformed cosine function. Let's analyze the key aspects:

1. **Amplitude**: The graph oscillates between 2 and -2, indicating the amplitude is 2.
2. **Period**: The graph completes one full cycle between 0 and 360 degrees, indicating the period is 360 degrees.

The general form of a cosine function is \( y = A \cos(Bx) \), where:
- \( A \) is the amplitude (which is 2 here).
- The period is given by \( \frac{360^\circ}{B} \). Since the period is 360 degrees, \( B = 1 \), meaning there is no horizontal compression/stretching.

### Answer:
The correct equation that matches this graph is \( 2 \cos(x) \), which corresponds to option **A**.

Would you like more details or have any questions? Here are some related questions:

1. What is the general form of a trigonometric function and how does each parameter affect the graph?
2. How do you determine the amplitude and period from a trigonometric graph?
3. What is the difference between the graphs of \( \cos(x) \) and \( \sin(x) \)?
4. How does changing the coefficient of \( x \) in \( \cos(Bx) \) affect the graph?
5. How do horizontal shifts affect the graph of trigonometric functions?

**Tip**: To quickly identify the function from a trigonometric graph, check the amplitude (maximum/minimum values) and the period (distance for one full cycle).

Which of the following trigonometric functions is displayed in the graph shown?

Analyze the trigonometric graph representing the function 2cos(x). Learn about the amplitude, period, and how transformations affect cosine graphs. Suitable for high school students studying trigonometry.

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