Question

Consider the function f(x) Answer the prompts by filling in each blank.

The average rate of change of f(x)over the interval (−3,−1) is .


The average rate of change of f(x) over the interval (−3,1) is .


The average rate of change of f(x) over the interval (−1,2) is .

Here are the choices to fit it in the box: -1 , -2/3, -1/2, 0 , 1/2, 2/3, 1

Answer 1

• (-3, -1) — 1/2
• (-3, 1) — 3/4
• (-1, 2) — 2/3

Explanation:

You want the average rate of change of the graphed function on the given intervals.

Average rate of change

The average rate of change is the "rise" over the interval, divided by the "run", the length of the interval.

(-3, -1)

The rise is from -2 at the left end to -1 at the right end, a rise of 1 unit. The width of the interval is -1 -(-3) = 2.

The average rate of change is 1/2.

(-3, 1)

The rise is from -2 at the left end to 1 at the right end, a rise of 3 units. The width of the interval is 1 -(-3) = 4.

The average rate of change is 3/4.

(-1, 2)

The rise is from -1 at the left end to 1 at the right end, a rise of 2 units. The width of the interval is 2-(-1) = 3 units.

The average rate of change is 2/3.

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