Question

This table shows the value of a function f(x)

What is the average rate of change of f(x) from -1 to 1?

Answer 1

12

Explanation:

We are given a table which holds the the values for a f(x) against every value of x.

We are to find the average rate of change of f(x) from the values of x -1 to 1.

Avg. rate of change from 1 to -1 =
`\frac { 27 - 3 } { 2 } = \frac { 24 } { 2 } = 12`

Therefore, the average rate of change of f(x) from -1 to 1 is 12 which means for each unit of x, there is an increase of 12 units in f(x).

Answer 2

12

Explanation:

Average rate of a function f(x) in the interval a to b is given by

Average rate of change =
`(f(b)-f(a))/(b-a)`

Here since end points are -1 and 1, we have

a=-1 and b=1

b-a = 2

`f(-1) =3\\f(1) = 27\\f(1)-f(-1) =27-3 =24`

Dividing we get

average rate of change

= 24/2 =12

On an average for 1 unit increase of x , f increases by 12 units.