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Use the Vertical Line Test to determine whether the graph represents y as a function of x.

Yes, y is a function of x.
No, y is not a function of x. 

To determine if the graph represents \( y \) as a function of \( x \), we can apply the **Vertical Line Test**. This test states that for \( y \) to be a function of \( x \), any vertical line drawn on the graph should intersect the curve at most **once**. 

Looking at the graph you provided, which is a circle centered at the origin with a radius of 4, a vertical line drawn at any \( x \)-value (except at the farthest left or right points) will intersect the circle **twice** — once above and once below the x-axis. 

Since a vertical line intersects the graph more than once, **y is not a function of x** in this case.

Let me know if you need any further clarification!

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Here are five related questions to expand on this concept:
1. What is the equation of the circle shown in the graph?
2. Can a circle ever represent \( y \) as a function of \( x \)?
3. What other shapes fail the Vertical Line Test, and why?
4. How can we modify this graph to make \( y \) a function of \( x \)?
5. What is the domain and range of the equation of this circle?

**Tip:** The Vertical Line Test is useful for quickly determining if a relation is a function, but it’s also essential to know the algebraic form of the relation for deeper analysis.

Use the Vertical Line Test to determine whether the graph represents y as a function of x.

Explore how to apply the Vertical Line Test to a circle's graph to determine whether y is a function of x. This problem reviews the equation of a circle and the concept of a function in mathematics, ideal for students in Grades 9-12.

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