To determine if the graph represents a function, we can apply the vertical line test. This test states that if a vertical line intersects the graph at more than one point at any given x-value, then the graph does not represent a function. If each vertical line intersects the graph at only one point, then the graph represents a function.

Analysis:

In this graph, there are points along the x-axis where a vertical line would intersect the curve in two places (one intersection above the x-axis and one below it). Therefore, this graph fails the vertical line test.

Conclusion:

• Answer: This relation does not pass the vertical line test and is not a function.

Would you like further details on the vertical line test or any other concept?

Here are some related questions that might help you understand this topic further:

1. What other methods can we use to determine if a relation is a function?
2. How does the vertical line test apply to different types of graphs, such as parabolas or circles?
3. Can a function have an inverse that fails the vertical line test?
4. Why is the vertical line test useful in determining functions in coordinate geometry?
5. How does failing the vertical line test relate to one-to-one and many-to-one relationships?

Tip: For functions represented by equations, rearrange them into y = f(x) form to check if each x-value has only one corresponding y-value.