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The correct answers for the characteristics of the function \( y = \cos x \) are:

1. **Periodic function with a period of \( 2\pi \)**: The cosine function is indeed periodic with a period of \( 2\pi \).
2. **Even function**: \( \cos x \) is an even function, as it satisfies \( \cos(-x) = \cos(x) \).
3. **Range: \([-1, 1]\)**: The range of the cosine function is bounded between -1 and 1.
4. **Symmetric with respect to the y-axis**: Since \( \cos x \) is an even function, its graph is symmetric with respect to the y-axis.
5. **Domain: \((-\infty, \infty)\)**: The cosine function is defined for all real values of \( x \), so its domain is \((-\infty, \infty)\).

Thus, the checked boxes should be:
- Periodic function with a period of \( 2\pi \)
- Even function
- Range: \([-1, 1]\)
- Symmetric with respect to the y-axis
- Domain: \((-\infty, \infty)\)

Would you like more details on any of these properties? 

### Related Questions
1. Why is \( y = \cos x \) not considered an odd function?
2. How does the periodicity of \( y = \cos x \) differ from other trigonometric functions?
3. What are some other examples of even functions?
4. How does symmetry affect the graph of an even function?
5. Why is the range of \( y = \cos x \) limited to \([-1, 1]\)?

### Tip
Remember, even functions are always symmetric with respect to the y-axis, while odd functions are symmetric with respect to the origin.

The graph of y = cos(x) has the following characteristics. [Check all that apply.]

Explore the properties of the cosine function y = cos(x), including its periodicity, symmetry, range, and domain. This problem is suitable for high school students learning trigonometry and function properties.

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