To determine whether an equation describes $y$ as a function of $x$, we need to check if for every value of $x$, there is exactly one corresponding value of $y$. In other words, for $y$ to be a function of $x$, each input $x$ should map to only one output $y$.

Common ways to test:

1. Solve for $y$: Try to express $y$ explicitly in terms of $x$. If you can get a single expression for $y$ (not two different expressions), $y$ is likely a function of $x$.
2. Vertical Line Test: If the equation is graphed, a vertical line should intersect the graph at most once for any given value of $x$. If a vertical line crosses the graph more than once, then $y$ is not a function of $x$.

Example:

• Linear equation: $y = 2x + 3$ describes $y$ as a function of $x$ because for every $x$, there is exactly one $y$.
• Circle equation: $x^2 + y^2 = 1$ does not describe $y$ as a function of $x$, because for some values of $x$, there are two different corresponding values of $y$ (e.g., when $x = 0$, $y = 1$ or $y = -1$).

If you have a specific equation in mind, please share it, and I can analyze it further.

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Do you have any questions or would you like more details on this? Here are some related questions you might consider:

1. How can you determine if a relation is a function from a table of values?
2. What are the key characteristics of a function?
3. How does the Vertical Line Test work for different types of graphs?
4. Can an equation involve $y$ and still not describe $y$ as a function of $x$?
5. How do you identify the domain and range of a function?

Tip: Always try to solve for $y$ and see if it can be expressed as a single value in terms of $x$ to quickly check if the equation is a function.