The image shows a graph and a question asking to determine whether the graph represents a function.

Let's analyze this:

1. Function Definition: A graph represents a function if, for every $x$ value, there is exactly one $y$ value. This is known as the vertical line test. If a vertical line crosses the graph at more than one point, the graph does not represent a function.

2. Applying the Vertical Line Test: Looking at the graph in the image, we see that it is a parabola that opens downwards. If we imagine drawing vertical lines across the graph, each vertical line will intersect the graph at exactly one point.

Conclusion:

• Since every vertical line intersects the graph at exactly one point, the graph does represent a function.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How does the vertical line test help in determining if a graph represents a function?
2. What are the different types of functions, and how do their graphs differ?
3. How can you determine the domain and range of a function from its graph?
4. What is the significance of the vertex in the graph of a quadratic function?
5. How can we distinguish between a linear and a quadratic function based on their graphs?

Tip: When analyzing graphs, always check the behavior of the function as $x$ approaches infinity and negative infinity to understand its overall shape and direction.