Question

PLEASE HELP

Match each interval with its corresponding average rate of change for the graph shown below.


1. 0 ≤ x ≤ 1 -0.375

2. -2 ≤ x ≤ -1 -1.5

3. -2 ≤ x ≤ 0 -0.5

4. 1 ≤ x ≤ 2 -0.25

5. -1 ≤ x ≤ 0 -2

6. 0 ≤ x ≤ 2 -1

Answer 1

0 ≤ x ≤ 1 = -0.5

-2 ≤ x ≤ -1 = -2

-2 ≤ x ≤ 0 = -1.5

1 ≤ x ≤ 2 = -0.25

-1 ≤ x ≤ 0 = -1

0 ≤ x ≤ 2 = -0.375

Explanation:

simplified from the other response.

Answer 2

It is convenient to work with pairs of points on the graph from right to left.

Between 1 and 2, the graph goes over 4 and down 1, so the slope is -1/4

Between 0 and 1, the graph goes over 4 and down 2, so the slope is -2/4 = -1/2

We can see a trend here. For each unit interval farther to the left, the slope doubles. So, we have ...

1 ≤ x ≤ 2 : -0.25

0 ≤ x ≤ 1 : -0.5

-1 ≤ x ≤ 0 : -1

-2 ≤ x ≤ -1 : -2

The average slope over the longer intervals will be the average of the slopes in the (same length) intervals that make up the longer 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

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Going by the numbers on your list here, the matching (interval, slope) pairs are ... (1, 3), (2, 5), (3, 2), (4, 4), (5, 6), (6, 1)