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!

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.