Question

What is the average rate of change of the function described by the table below over the interval

[−1,3]?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the average rate of change of a function over an interval, we need to calculate the change in the function's values divided by the change in the interval.

First, let's look at the given table:

x | f(x)
-1| 2
0 | 5
2 | 8
3 | 10

Since the interval is from -1 to 3, the change in the interval is 3 - (-1) = 4.

Now, let's calculate the change in the function's values:
f(3) - f(-1) = 10 - 2 = 8

Finally, we can find the average rate of change:
Average rate of change = change in values / change in interval
Average rate of change = 8 / 4 = 2

Therefore, the average rate of change of the function over the interval [-1,3] is 2.