https://file.aiquickdraw.com/mathbot/file/1728949034736nnk71ja1.jpg

To determine which relation is a function, we can apply the **vertical line test**. This test checks whether any vertical line drawn through the graph intersects the relation at more than one point. If it does, the relation is **not** a function. A function can only assign one output (y-value) to each input (x-value).

### Let's analyze the graphs:

1. **Top-left graph**: 
   - At x = 2 and x = -2, vertical lines intersect multiple points on the graph. This means the relation **fails** the vertical line test, so it is **not** a function.

2. **Top-right graph**:
   - A vertical line at any x-value only intersects at one point. This relation **passes** the vertical line test, meaning it **is** a function.

3. **Bottom-left graph**:
   - At x = 0, a vertical line intersects more than one point. This fails the vertical line test, so it is **not** a function.

4. **Bottom-right graph**:
   - At x = -2, vertical lines intersect more than one point. This also fails the vertical line test, so it is **not** a function.

### Conclusion:
The **top-right graph** represents a function because it passes the vertical line test.

Would you like more details on any part of the explanation? 

Here are 5 related questions to explore:
1. What is the vertical line test, and why does it work for determining functions?
2. Can a relation that is not a function still be useful in mathematics?
3. How do you define the domain and range of a function using a graph?
4. What is the difference between a relation and a function?
5. How can you identify a function from its equation rather than its graph?

**Tip:** A relation is a function if each x-value has only one corresponding y-value.

Learn how to identify a function using the vertical line test. Analyze graphical relations to determine whether each relation is a function by checking if vertical lines intersect the graph more than once. Suitable for students in Grades 8-10.

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