To determine if the given relation is a function, we need to apply the vertical line test.

Analyzing the Graph:

• The graph in the image shows a curve that opens to the right.
• To apply the vertical line test, we need to check if any vertical line drawn through the graph intersects it at more than one point.

Vertical Line Test:

• A relation is a function if every vertical line intersects the graph at most one point.
• Looking at the graph provided, if we draw a vertical line (say $x = 1$), this line will intersect the graph at exactly one point.

Conclusion:

• Yes, it passes the vertical line test, meaning the graph represents a function.

However, the horizontal line test is used to determine if a function is one-to-one, not if a relation is a function. The horizontal line test is irrelevant in this context for determining whether the relation is a function.

Answer:

Yes, it passes the vertical line test. The relation shown in the graph is a function.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is the horizontal line test, and when do we use it?
2. How do we determine if a function is one-to-one using a graph?
3. What are some examples of graphs that do not pass the vertical line test?
4. Can a curve that opens to the left also represent a function?
5. What is the difference between a relation and a function?

Tip: Remember that the vertical line test is a quick way to determine if a relation is a function. If any vertical line crosses the graph more than once, the relation is not a function.