The question in this image is asking which of the given graphs represents a function.

To determine whether each option represents a function, we can apply the vertical line test. According to this test, if a vertical line intersects the graph at more than one point, the graph is not a function. Let’s analyze each option:

1. Option A: This graph is a circle. Any vertical line passing through the center of the circle will intersect it at two points. Therefore, this is not a function.

2. Option B: This graph shows a parabola opening upwards. A vertical line will intersect it at only one point for any given $x$-value. This is a function.

3. Option C: This graph appears to be a curve that intersects itself, resembling a sideways figure-eight. A vertical line would intersect it at more than one point in some regions. This is not a function.

4. Option D: This is a sideways parabola. A vertical line can intersect it at two points, so this is not a function.

Based on this analysis, Option B is the correct answer because it is the only graph that passes the vertical line test and thus represents a function.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the vertical line test and why does it determine if a graph is a function?
2. How can we define a function formally in terms of ordered pairs?
3. What are some common types of graphs that are not functions?
4. How does the horizontal line test relate to one-to-one functions?
5. What are some real-life examples of functions and non-functions?

Tip: When graphing, always check if the graph passes the vertical line test to quickly identify if it represents a function.