Question

A teacher notices a correlation between students’ scores on homework assignments and their scores on corresponding quizzes. The line of best fit for the data is given by the formula q=1.2h−25 , where h is the student homework score and q is the student quiz score. Which of the following relates the domain of this function to this scenario? (Assume that the homework does not have extra credit).(1 point) Responses [−25,25] left bracket negative 25 comma 25 right bracket [0,1.2] left bracket 0 comma 1.2 right bracket [50,90] left bracket 50 comma 90 right bracket [0,100]

Answer 1

To determine the appropriate domain of the function relating the homework scores (h) to the quiz scores (q), we should consider the typical scoring range for homework assignments and quizzes.

In a standard educational context, homework scores (h) and quiz scores (q) would typically range from 0 to 100. This is common in many grading systems where scores are scaled from 0 (lowest) to 100 (highest).

Since the formula for the line of best fit is \( q = 1.2h - 25 \), we can analyze what happens when h takes on values within the conventional range:

1. If \( h = 0 \):
   \( q = 1.2(0) - 25 = -25 \) (not a valid score)

2. If \( h = 100 \):
   \( q = 1.2(100) - 25 = 120 - 25 = 95 \) (valid score)

To be within the valid scoring range for quizzes, we need to ensure that \( q \) stays within \( [0, 100] \).

However, since the lowest possible value for the homework score 'h' (typically) would be 0 and the highest would be 100, we can conclude that:

The appropriate domain for homework scores in this context is \( [0, 100] \).

Thus, the answer is:

[0, 100]