https://file.aiquickdraw.com/mathbot/file/1728693009911pii5jmr4.jpg

The graph shown appears to represent a trigonometric function, possibly a cosine function, since it exhibits a wave-like pattern with symmetry about the origin. Here's the interpretation based on the image:

- **Domain**: The domain of the function in this graph covers the horizontal extent. The graph spans from \( -\pi \) to \( \pi \). Thus, the domain is:
  \[
  [-\pi, \pi]
  \]
  
- **Range**: The range is determined by the vertical extent of the graph. The maximum value reached by the curve is 1, and the minimum value is -1. Therefore, the range is:
  \[
  [-1, 1]
  \]

This graph resembles the cosine function \( y = \cos(x) \), which has this behavior in the interval \( [-\pi, \pi] \).

Would you like further details on how these values are determined?

### 5 Relative Questions:
1. What is the significance of the periodicity in trigonometric functions like cosine?
2. How do we determine the amplitude of trigonometric functions from a graph?
3. What are the key differences between the cosine and sine functions in terms of their graphs?
4. Can the domain of trigonometric functions like cosine extend to infinity?
5. How does the phase shift affect the cosine graph?

### Tip:
Always check for symmetry in trigonometric function graphs to identify key characteristics like amplitude, period, and phase shift more easily.

What's the domain and range of the function in the graph?

This problem demonstrates how to find the domain and range of a trigonometric cosine function in the interval [-π, π]. The graph shows that the domain is [-π, π], and the range is [-1, 1]. Explore key concepts in trigonometry and learn how to interpret the cosine function graph.

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