Question: Determine if the relation defines $y$ as a function of $x$.
Yes, this relation defines $y$ as a function of $x$.
No, this relation does not define $y$ as a function of $x$.
Graph: a single wavy curve on the x-y plane with a tall peak near $(0, 4)$, oscillating around $y = 0$ and passing the vertical line test; position_hint=center
1. **State the problem:** We need to determine if the given relation defines $y$ as a function of $x$.
2. **Recall the definition of a function:** A relation defines $y$ as a function of $x$ if and only if for every $x$-value there is exactly one corresponding $y$-value.
3. **Use the vertical line test:** The vertical line test states that if any vertical line intersects the graph more than once, then $y$ is not a function of $x$.
4. **Analyze the graph:** The graph is a single wavy curve with a tall peak near $(0, 4)$, oscillating around $y=0$.
5. **Check vertical line intersections:** Since the graph passes the vertical line test (no vertical line intersects the curve more than once), each $x$ corresponds to exactly one $y$.
6. **Conclusion:** Therefore, the relation defines $y$ as a function of $x$.
**Final answer:** Yes, this relation defines $y$ as a function of $x$.