https://file.aiquickdraw.com/mathbot/file/17282754552434ykvy89y.jpg

To determine whether the graphed relation defines a function, we need to apply the **vertical line test**. According to this test, a graph represents a function if and only if every vertical line drawn through the graph intersects it at most once.

### Analysis of the Graph:
The graph provided has a wave-like curve. When you apply the vertical line test:
- If any vertical line drawn intersects the curve more than once, the relation is **not a function**.
- If every vertical line intersects the curve **only once**, then the relation **is a function**.

In this graph, you can see that there are multiple points where vertical lines would intersect the graph more than once. For example, if you draw a vertical line at \(x = 1\), it would intersect the graph in two places, meaning that for the same \(x\)-value, there are two different \(y\)-values.

### Conclusion:
Since there are vertical lines that intersect the graph at more than one point, **the graphed relation does not define a function**.

#### Domain and Range:
- **Domain**: The graph spans from approximately \(x = -10\) to \(x = 10\), so the domain can be written as \([-10, 10]\).
- **Range**: The graph ranges from approximately \(y = -10\) to \(y = 10\), so the range can be written as \([-10, 10]\).

Would you like more details on this analysis, or do you have any questions?

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Here are some related questions that might expand on this topic:
1. What is the vertical line test and how is it applied in different types of graphs?
2. How do we find the domain and range for a relation on a graph?
3. What are some examples of relations that are not functions?
4. Can a function have multiple \(y\)-values for the same \(x\)-value? Why or why not?
5. How can we determine if a function is one-to-one using a horizontal line test?

**Tip:** Always remember that a function will pass the vertical line test, which means no vertical line can intersect the graph more than once at any point.

Does the graphed relation define a function?

Learn how to determine if a graphed relation defines a function by applying the vertical line test. Understand key concepts like domain and range with a graph that spans from x = -10 to x = 10 and y = -10 to y = 10. Suitable for Grades 8-10.

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