Match each interval with its corresponding average rate of change for q(x) = (x + 3)2. 1. -6 ≤ x ≤ -4 3 2. -3 ≤ x ≤ 0 0 3.

It is convenient to work with pairs of points on the graph from right to left. Between 1 and 2, the graph goes through 4 and goes down by 1, so the slope is -1/4 Between 0 and 1, the graph goes through 4 and goes down by 2, so the slope is -2/4 = – 1/2 can see a trend here. For each leftmost unit interval, the slope doubles. We therefore have … 1 ≤ x ≤ 2: -0.25 0 ≤ x ≤ 1: -0.5 -1 ≤ x ≤ 0: -1 -2 ≤ x ≤ -1: -2 The average slope over the longest intervals will be the average slopes in the intervals (of the same length) that make up the longest interval. -2 ≤ x ≤ 0: average of -2 and -1, so -1.5 0 ≤ x ≤ 2: average of -0.5 and -0.25, so -0.375 Going through the numbers in your list here, the matching (range, slope) pairs are… (1, 3), (2, 5), (3, 2), (4, 4), (5, 6), (6, 1)

Walkthrough: 1. cannot answer because there is no positive number 2. -1.5, -1, -2 3. -2, -1.5, -1 4. again cannot answer because there is there is no positive number 5. -1, -5, -0.375, -0.25 6. again there is no answer because there is no positive number