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]

1 answer

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]