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To determine whether the graphed relation is a function or not, we use the **Vertical Line Test**:

- A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Let’s analyze each graph:

1. **Top Graph**: The graph is a parabola. Applying the vertical line test, some vertical lines (e.g., near the vertex) intersect the graph twice. Therefore, **this is NOT a function**.

2. **Middle Graph**: This graph is a curve extending upwards. Some vertical lines will intersect the graph at more than one point (e.g., near the center of the curve). **This is NOT a function**.

3. **Bottom Graph**: This graph is a straight line. Any vertical line intersects the graph only once. **This IS a function**.

Would you like further clarification or detailed explanations? Let me know if you have more questions!

Here are related questions to deepen your understanding:

1. What is the definition of a function in mathematics?
2. How does the vertical line test work for identifying functions?
3. Are all straight-line graphs always functions? Why or why not?
4. How can you algebraically confirm if a relation is a function?
5. Can a relation fail the vertical line test but still have some functional properties?

**Tip**: Always visualize or sketch graphs if unsure about the vertical line test—it’s an intuitive and reliable method!

For each graph below, determine whether the relation graphed is a function or not.

Learn how to determine if a graph represents a function using the Vertical Line Test. Analyze different types of graphs, including parabolas and linear graphs, with a step-by-step explanation. Suitable for Grades 8-10.

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