To determine which relation is a function, we can apply the vertical line test. This test checks whether any vertical line drawn through the graph intersects the relation at more than one point. If it does, the relation is not a function. A function can only assign one output (y-value) to each input (x-value).

Let's analyze the graphs:

1. Top-left graph:

   • At x = 2 and x = -2, vertical lines intersect multiple points on the graph. This means the relation fails the vertical line test, so it is not a function.

2. Top-right graph:

   • A vertical line at any x-value only intersects at one point. This relation passes the vertical line test, meaning it is a function.

3. Bottom-left graph:

   • At x = 0, a vertical line intersects more than one point. This fails the vertical line test, so it is not a function.

4. Bottom-right graph:

   • At x = -2, vertical lines intersect more than one point. This also fails the vertical line test, so it is not a function.

Conclusion:

The top-right graph represents a function because it passes the vertical line test.

Would you like more details on any part of the explanation?

Here are 5 related questions to explore:

1. What is the vertical line test, and why does it work for determining functions?
2. Can a relation that is not a function still be useful in mathematics?
3. How do you define the domain and range of a function using a graph?
4. What is the difference between a relation and a function?
5. How can you identify a function from its equation rather than its graph?

Tip: A relation is a function if each x-value has only one corresponding y-value.