https://file.aiquickdraw.com/mathbot/file/1729553474887tpoji9n8.jpg

The problem asks which of the given graphs represent functions. To determine if a graph represents a function, we can use the **Vertical Line Test**. This test states that if a vertical line passes through more than one point on the graph, then the graph is *not* a function.

Let’s evaluate each graph:

1. **Top-left graph**: This is a straight diagonal line. A vertical line will intersect this graph at exactly one point for any value of \(x\), so it **is a function**.
   
2. **Top-right graph**: This is a curved line (possibly part of a quadratic function). A vertical line will only intersect the curve at one point for any value of \(x\), so it **is a function**.

3. **Bottom-left graph**: This is a V-shaped graph (possibly an absolute value function). A vertical line will intersect the graph at only one point for each \(x\)-value, so it **is a function**.

4. **Bottom-right graph**: This is a wavy line. If you draw a vertical line, it can intersect the graph at more than one point for some \(x\)-values, so it **is not a function**.

### Conclusion:
- The graphs that **are functions** are:
  - Top-left (diagonal line)
  - Top-right (curved line)
  - Bottom-left (V-shape)

Would you like more details on the Vertical Line Test or functions? Let me know!

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Here are 5 related questions:
1. How does the vertical line test help in identifying functions?
2. Can all linear graphs be considered functions?
3. How would you define a function in mathematical terms?
4. What are the key differences between a function and a relation?
5. Are there exceptions to the Vertical Line Test for special types of functions?

**Tip**: When analyzing graphs, always remember that functions can only assign one output (y-value) for each input (x-value).

Which of these relations are functions? Select all that apply.

Learn how to determine whether given relations are functions using the Vertical Line Test. Analyze graphs to see if a vertical line intersects at more than one point for any x-value. This problem covers fundamental concepts of functions and graph analysis, suitable for students in Grades 7-10.

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