https://file.aiquickdraw.com/mathbot/file/1729550699901neofxcb2.jpg

The image asks to use the vertical line test to determine if the graph shown represents \( y \) as a function of \( x \).

### Vertical Line Test:
The vertical line test is a way to determine if a graph represents a function. To use it:
- If any vertical line intersects the graph at **more than one point**, the graph does **not** represent a function.
- If a vertical line intersects the graph at **only one point** everywhere, then the graph does represent a function.

### Given Graph:
In the graph shown, there is a vertical line which intersects the graph (the vertical axis) at **multiple points** along the same vertical line. This means that for one value of \( x \), there are multiple values of \( y \). 

### Conclusion:
This graph does **not** represent \( y \) as a function of \( x \), because the vertical line intersects the graph at more than one point.

So, the correct sentence would be:

"The graph **is not** a graph in which \( y \) is a function of \( x \), because a vertical line can be drawn such that it intersects the graph in more than one point."

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Would you like any further clarification or details?

Here are five related questions for further exploration:
1. What is the horizontal line test and how is it different from the vertical line test?
2. Can a graph represent a function of \( y \) instead of \( x \)? How would that change the test?
3. What are some real-life examples of graphs that fail the vertical line test?
4. How can we algebraically verify if an equation represents a function?
5. Can a relation be a function in one direction but not in the other?

**Tip**: Always remember, a function assigns exactly one output (y) for each input (x), which is why the vertical line test works!

Use the vertical line test to determine whether the given graph is a graph in which y is a function of x.

Learn how to apply the vertical line test to determine if a graph represents y as a function of x. This test helps students understand functions, graphing, and the relationship between x and y values. Ideal for Grades 8-10.

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