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To determine whether the graph represents a function, we can apply the **vertical line test**. According to this test, if a vertical line intersects the graph at more than one point, then the graph does not represent a function.

In the provided graph, if you imagine drawing vertical lines at different values of \( x \), you will see that each vertical line intersects the graph at two points. This means that for some values of \( x \), there are two corresponding \( y \) values.

Since a function can only have one output (i.e., one \( y \) value) for each input (i.e., each \( x \) value), this graph **does not** represent a function.

Would you like more details or have any other questions? Here are some related questions you might find interesting:

1. What is the horizontal line test, and how does it relate to determining if a function is one-to-one?
2. Can you describe the characteristics of a graph that would pass the vertical line test?
3. How do we mathematically define a function?
4. What is the difference between a function and a relation in mathematics?
5. How would you graphically represent a piecewise function?

**Tip:** When determining if a graph represents a function, always check if each input (x-value) corresponds to exactly one output (y-value) by using the vertical line test.

Learn how to determine if a graph represents a function using the vertical line test. This problem involves analyzing graphs and applying mathematical concepts related to functions. Suitable for high school students studying algebra and graph theory.

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