Question

What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]?

x    f(x)
-6  2.5
-2  2.5
0      2
2      0
3      5


answers:
A.  5
B. 2.5
C. 1
D. 0.5

Answer 1

D. 0.5

Explanation:

We will use average rate of change to solve our given problem.

`\text{Average rate of change}=(f(b)-f(a))/(b-a)`

The average rate of change between -2 and 3 would be:

`\text{Average rate of change}=(f(3)-f(-2))/(3--2)`

Upon looking at our given table we can see that
`f(3)=5` and
`f(-2)=2.5`.

`\text{Average rate of change}=(5-2.5)/(3+2)`

`\text{Average rate of change}=(2.5)/(5)`

`\text{Average rate of change}=0.5`

Therefore, the average rate of change over closed interval
`[-2,3]` is 0.5 and option D is the correct choice.

Answer 2

Average rate of change = (f(b) - f(a))/(b - a) = (f(3) - f(-2))/(3 - (-2)) = (5 - 2.5)/(3 + 2) = 2.5/5 = 0.5