https://file.aiquickdraw.com/mathbot/file/1726878725917vrn9ichj.jpg

This graph appears to show a curve that fails the **vertical line test**, meaning it is not the graph of a function.

The **vertical line test** states that if any vertical line drawn through the graph intersects the curve at more than one point, the curve is not the graph of a function. In this image, vertical lines can intersect the curve in more than one place (e.g., near \(x = -2\) and \(x = 2\)). Therefore, this is not the graph of a function.

Would you like further details or any clarifications on this concept?

### Related Questions:
1. What is the vertical line test, and why is it important?
2. How do we determine if a relation is a function?
3. Can you provide examples of graphs that represent functions?
4. What is the difference between functions and relations in mathematics?
5. How would this graph change to become a function?

### Tip:
When identifying functions, remember that each input (x-value) must correspond to exactly one output (y-value).

This guide explains how to determine whether a curve represents a function using the vertical line test. The example graph shows a curve that fails the vertical line test, meaning it is not a function. Explore the mathematical concepts behind functions and relations, with real-world examples and detailed explanations.

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