The question asks if the relation depicted in the graph defines $y$ as a function of $x$. To determine this, we can use the vertical line test:

Vertical Line Test:

• A relation defines $y$ as a function of $x$ if and only if no vertical line intersects the graph at more than one point.
• If any vertical line intersects the graph at more than one point, then $y$ is not uniquely determined by $x$, and the relation does not define $y$ as a function of $x$.

Analysis of the Graph:

From the image:

1. The curve appears to have parts where a vertical line would intersect it in more than one place. For example:
   • Near $x = 0$, a vertical line intersects the graph at two points, one in the upper part of the curve and one in the lower part.
   • This indicates that for certain values of $x$, there are multiple corresponding values of $y$.

Conclusion:

The relation does not define $y$ as a function of $x$. Therefore, the correct answer is:

• No, this relation does not define $y$ as a function of $x$.

Would you like a deeper explanation of the vertical line test or how functions are defined?

Here are 5 questions that expand on this topic:

1. What is the difference between a function and a general relation?
2. How does the horizontal line test differ from the vertical line test?
3. Can a graph be a function of $x$ but not a function of $y$?
4. How can piecewise functions be represented graphically to satisfy the definition of a function?
5. How do implicit functions differ from explicit functions?

Tip:

Remember, a function assigns exactly one output for each input, which is why the vertical line test works to check this visually!