The vertical line test is used to determine if a relation is a function by checking if any vertical line intersects the graph at more than one point. If a vertical line intersects the graph in more than one place, then the graph does not represent a function. If every vertical line intersects the graph at most once, then it does represent a function.

In the provided graph:

1. For $x < 0$, each vertical line intersects the curve only once.
2. For $x > 0$, each vertical line also intersects the curve only once.

Since no vertical line intersects the graph at more than one point, this graph passes the vertical line test and therefore represents a function.

Answer:

• The correct option is:
  • This relation passes the vertical line test and is a function.

Would you like a detailed explanation of the vertical line test?

Related Questions:

1. What are some examples of graphs that do not pass the vertical line test?
2. How does the horizontal line test differ from the vertical line test?
3. Can a graph fail the vertical line test and still be useful in mathematics?
4. How can transformations affect whether a graph passes the vertical line test?
5. Are there any cases where a relation fails the vertical line test at only one point?

Tip:

When in doubt, sketching or visualizing a vertical line moving across the graph can help determine if a relation is a function.