https://file.aiquickdraw.com/mathbot/file/1725906646962zgteaioe.jpg

The image you've uploaded shows a graph with two curves and a vertical line. To determine if this represents a function, we can use the **vertical line test**.

### Vertical Line Test:
A graph represents a function if and only if **any vertical line** drawn through the graph intersects it at most once. This ensures that for each input \( x \), there is only one output \( y \).

### Applying it to the Graph:
- There is a vertical line shown on the right side of the graph.
- This vertical line intersects the graph at **two points**, meaning there are two outputs for the same \( x \)-value.

### Conclusion:
Since the vertical line intersects the graph at more than one point, **this graph does not represent a function**. The graph fails the vertical line test.

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

Here are 5 related questions:
1. How do you perform a vertical line test on more complex graphs?
2. What is the definition of a function in terms of domain and range?
3. How can you algebraically determine if an equation represents a function?
4. What are some common types of graphs that fail the vertical line test?
5. How does the concept of a function apply in real-world problems?

**Tip:** The vertical line test is a quick visual way to check if a graph represents a function, but for more complicated equations, algebraic methods are often more reliable.

Determine if the given graph represents a function using the vertical line test.

This article explores the vertical line test and how to use it to determine whether a graph represents a function. In this example, the test is applied to a graph with two curves and a vertical line, explaining why the graph does not pass the test.

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