https://file.aiquickdraw.com/mathbot/file/1724669187631s5t5qvo4.jpg

Determine if the following relation is a function and explain why.

No, it doesn't pass the horizontal line test

Yes, it passes the horizontal line test

No, it doesn't pass the vertical line test

Yes, it passes the vertical line test

To determine if the given relation is a function, we need to apply the **vertical line test**. 

### Analyzing the Graph:
- The graph in the image shows a curve that opens to the right.
- To apply the **vertical line test**, we need to check if any vertical line drawn through the graph intersects it at more than one point.

### Vertical Line Test:
- A relation is a function if **every vertical line** intersects the graph at **most one point**.
- Looking at the graph provided, if we draw a vertical line (say \(x = 1\)), this line will intersect the graph at exactly one point.

### Conclusion:
- **Yes, it passes the vertical line test**, meaning the graph represents a function.
  
However, the horizontal line test is used to determine if a function is **one-to-one**, not if a relation is a function. The horizontal line test is irrelevant in this context for determining whether the relation is a function.

### Answer:
**Yes, it passes the vertical line test.** The relation shown in the graph is a function.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What is the horizontal line test, and when do we use it?
2. How do we determine if a function is one-to-one using a graph?
3. What are some examples of graphs that do not pass the vertical line test?
4. Can a curve that opens to the left also represent a function?
5. What is the difference between a relation and a function?

**Tip:** Remember that the vertical line test is a quick way to determine if a relation is a function. If any vertical line crosses the graph more than once, the relation is not a function.

Learn how to determine if a relation is a function by applying the vertical line test. Understand the concept and its application with examples. Suitable for students in Grades 9-12.

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