https://file.aiquickdraw.com/mathbot/file/1725407346394i50gm1fe.jpg

The image shows a graph and a question asking to determine whether the graph represents a function.

### Let's analyze this:
1. **Function Definition**: A graph represents a function if, for every \(x\) value, there is exactly one \(y\) value. This is known as the vertical line test. If a vertical line crosses the graph at more than one point, the graph does not represent a function.

2. **Applying the Vertical Line Test**: Looking at the graph in the image, we see that it is a parabola that opens downwards. If we imagine drawing vertical lines across the graph, each vertical line will intersect the graph at exactly one point.

### Conclusion:
- Since every vertical line intersects the graph at exactly one point, the graph **does** represent a function.

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:
1. How does the vertical line test help in determining if a graph represents a function?
2. What are the different types of functions, and how do their graphs differ?
3. How can you determine the domain and range of a function from its graph?
4. What is the significance of the vertex in the graph of a quadratic function?
5. How can we distinguish between a linear and a quadratic function based on their graphs?

**Tip**: When analyzing graphs, always check the behavior of the function as \(x\) approaches infinity and negative infinity to understand its overall shape and direction.

Determine whether the graph represents y as a function of x.

Analyze a graph to determine if it represents y as a function of x using the Vertical Line Test. Learn the core concepts and methods to assess whether a graph passes the function test. Suitable for students in Grades 9-12.

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