Here is the graph based on the assumption method, along with the full circle for context. The red points represent the specific values we assumed for $x$ and their corresponding $y$ values.

Step 3: Determine if $y$ is a Function of $x$

As we observed earlier, for most values of $x$, there are multiple $y$ values (one positive and one negative). This violates the requirement for a function, where each $x$ value should correspond to exactly one $y$ value. Therefore, $y$ is not a function of $x$.

Would you like further details or have any questions?

Related Questions:

1. What happens if we assume negative values of $x$? How does it affect $y$?
2. How would the solution change if we assumed non-integer values for $x$?
3. Can the assumption method be applied to non-circular equations?
4. What is the range of $y$ for all possible $x$ values in this equation?
5. How does this assumption method help in understanding the shape of the graph?

Tip: The assumption method is a useful way to explore the behavior of an equation by testing specific values, especially when learning about the graph's shape and properties.