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The graph provided shows a cosine function that has undergone transformations. To determine the period of the function, we need to observe the interval required for one complete cycle of the curve.

Looking at the graph:

- The function starts at a peak at \( x = -2\pi \), goes down, reaches a minimum, and then comes back to a peak at \( x = 0 \). Another peak occurs at \( x = 2\pi \).
  
- The distance between two consecutive peaks is \( 2\pi \).

Thus, the period of the cosine function is **\( 2\pi \)**.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:

1. How do transformations affect the period of a cosine function?
2. What are the amplitude and vertical shift of the graphed cosine function?
3. Can you identify the phase shift of this cosine function from the graph?
4. What is the general form of a transformed cosine function, and how does it apply here?
5. How would the graph look if the period were halved?

**Tip:** The period of cosine and sine functions in their basic form is always \( 2\pi \), and changes to the period occur when a horizontal scaling is applied.

Identify the period of the graphed cosine function.

Learn how to determine the period of a graphed cosine function from -2π to 2π. This problem involves core trigonometric concepts, including periodicity and transformation of cosine functions. Suitable for high school students in Grades 10-12.

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