https://file.aiquickdraw.com/mathbot/file/1725900342332or5xfsat.jpg

To determine if the graphs in the image represent valid functions, we can apply the **vertical line test**. This test states that a graph represents a function if and only if every vertical line intersects the graph at most once.

Here is the analysis of each graph:

1. **Top Graph:**
   - The graph fails the vertical line test. For example, a vertical line at \( x = -4 \) intersects the graph at two points. Therefore, this is **not a valid function**.

2. **Middle Graph:**
   - This graph passes the vertical line test. Any vertical line intersects the graph at exactly one point. Therefore, this is a **valid function**.

3. **Bottom Graph:**
   - This graph also passes the vertical line test. Any vertical line intersects the graph at exactly one point. Therefore, this is a **valid function**.

**Summary:**
- Top Graph: Not a valid function.
- Middle Graph: Valid function.
- Bottom Graph: Valid function.

Would you like more details or have any further questions?

### Related Questions:
1. What is the vertical line test and why is it used to determine functions?
2. How can you algebraically verify if a relation is a function?
3. What are some examples of relations that are not functions?
4. How does the horizontal line test differ from the vertical line test?
5. Can a curve that fails the vertical line test be described by an equation?

**Tip:** Remember that functions can only assign one output for each input, which is why the vertical line test works.

Learn how to determine if graphs represent valid functions using the vertical line test. Analyze three different graphs to see which pass or fail the test, making this concept clear and easy to understand. Suitable for students in Grades 8-10.

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