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To determine if the given relation defines \( y \) as a function of \( x \), we need to check whether every input value of \( x \) has exactly one corresponding output value of \( y \).

The easiest way to verify this is by applying the **vertical line test**: if a vertical line drawn at any point along the graph intersects the graph in more than one place, then \( y \) is not a function of \( x \).

Looking at the graph, no vertical line would intersect the graph at more than one point for any \( x \)-value. Therefore, this relation **does define** \( y \) as a function of \( x \).

Thus, the correct answer is:
- **Yes, this relation defines \( y \) as a function of \( x \).**

Would you like more clarification or further questions?

Here are 5 follow-up questions:
1. How does the vertical line test work in identifying functions?
2. Can this function be represented by an equation?
3. What would happen if a vertical line intersected the graph at two points?
4. How can you use the horizontal line test to determine if a function is one-to-one?
5. What type of function (e.g., polynomial, trigonometric) does this graph likely represent?

**Tip:** A function passes the vertical line test if each \( x \)-value has only one \( y \)-value!

Determine if the relation defines y as a function of x based on the given graph.

Learn how to determine whether a relation defines y as a function of x using the vertical line test. Analyze the graph to see if each input has exactly one output. Suitable for students in Grades 9-12.

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