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