https://file.aiquickdraw.com/mathbot/file/17278404054641h3aqr4k.jpg

The graph you uploaded represents a sinusoidal curve, which appears to be a standard sine or cosine function. Let’s analyze the domain and range.

1. **Domain**: The domain of the sine or cosine function is all real numbers, since the function continues infinitely in both the positive and negative directions along the \(x\)-axis.
   \[
   \text{Domain}: (-\infty, \infty)
   \]

2. **Range**: The range of the sine or cosine function is limited between the maximum and minimum values that the curve reaches on the \(y\)-axis. From the graph, the curve oscillates between \(y = 1\) and \(y = -1\).
   \[
   \text{Range}: [-1, 1]
   \]

So, the domain is all real numbers, and the range is from \(-1\) to \(1\).

Would you like more details or have any questions about this? 

Here are 5 related questions you might find interesting:
1. What is the period of this sinusoidal function?
2. How do amplitude and phase shift affect the sine or cosine graph?
3. What is the general equation of a sinusoidal function?
4. Can this graph represent a real-world phenomenon? If yes, which one?
5. How would this graph change if the amplitude were doubled?

**Tip**: Always check the amplitude, period, and phase shift when analyzing or sketching sinusoidal graphs!

Understand how to determine the domain and range of sinusoidal functions such as sine and cosine. This detailed explanation covers the analysis of periodic curves, showing that the domain is all real numbers and the range is between -1 and 1. Suitable for high school students in Grades 9-12.

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