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To determine if the graph represents a function, we can use the **Vertical Line Test**. According to this test, a graph represents a function if and only if every vertical line drawn through the graph intersects it at no more than one point.

In the provided graph, we observe several points plotted in the coordinate plane. Let's check:

1. **Visual Inspection**: If you draw a vertical line through any x-value on the graph, it should only intersect the graph at one point for it to be a function.

Looking at the graph:

- A vertical line through \( x = 1 \) would intersect the graph at two points (around \( (1, 1) \) and \( (1, -3) \)).

Since there is at least one vertical line that intersects the graph at more than one point, **this graph does not represent a function**.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:

1. What are some examples of functions and non-functions?
2. How does the Vertical Line Test help in identifying functions?
3. Can you provide an example of a graph that is a function and explain why?
4. What are the implications of a graph failing the Vertical Line Test?
5. How do you determine the domain and range of a function graphically?

**Tip:** When analyzing a graph, always consider the behavior of all points with respect to the x-axis to apply the Vertical Line Test effectively.

Learn how to determine if a graph represents a function using the Vertical Line Test. Explore examples and implications of graphs that fail the test. Suitable for students in Grades 9-12.

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