This function models the number of points a student scores on a 10-point quiz as a function of the hours she spent playing video games the night before. Which of the following statements is correct?

To determine which statement is correct, we need to analyze the function that describes the relationship between the hours spent playing video games and the points scored on the quiz. However, since the specific function is not provided in your question, we can evaluate each statement based on what they imply:

1. **The point (10, 5) shows that the student earned 10 points on the quiz after playing video games for five hours.**
- This statement suggests that when the student plays video games for 5 hours, she scores 10 points. However, without the context of the function, we cannot confirm if this is true.

2. **There is a positive relationship between the number of points scored on the quiz and the number of hours spent playing video games.**
- This statement suggests that as the hours increase, the points also increase. If the function indicates that more hours of playing correlates with more points, then this would be true.

3. **The student’s quiz score goes down by one point for every two hours she spent on video games.**
- This statement suggests a negative relationship, where increased hours reduce scores. If the function indicates this, it would be true.

4. **The student will earn four points on the quiz if she plays eight hours of video games.**
- This claims a specific score based on the hours played. Like previous statements, without the function, this cannot be confirmed.

To conclude, without the specific function or additional information about the relationship, we cannot definitively say which of the statements is correct. However, if we had data that established the function, we could ascertain the accuracy of the statements based on that context.

If you're able to provide that function, I would be more than happy to analyze it further and determine which statement is true based on it!