Question

1. avg rate of change is 2 on the interval -1 ≤ x ≤ 1. avg rate of change is 7 on the interval 1 ≤ x ≤ 3. what is the average rate of change of g on the interval -3 ≤ x ≤ -1? -3 the avg rate of change is increasing by 5 for each interval of 2, but we must go \back\ to the interval -3 ≤ x ≤ -1 and decrease by 5.

Explanation:

Step1: Analyze rate change pattern

The average rate of change increases by 5 per interval of 2 (from \(-1\leq x\leq1\) to \(1\leq x\leq3\), change from 2 to 7, difference \(7 - 2 = 5\)).

Step2: Find rate for \(-3\leq x\leq -1\)

To get to the interval \(-3\leq x\leq -1\) from \(-1\leq x\leq1\), we move backward. So we decrease the rate of change by 5. The rate at \(-1\leq x\leq1\) is 2, so \(2 - 5=-3\).

Answer:

\(-3\)