Question

A function is shown in the table at the right. Find the rate of change over the interval 1≤ x≤ 3 .

Answer 1

Given:

The table of values of a function.

To find:

The rate of change of the function over the interval
`1\leq x\leq 3`.

Solution:

The rate of change of a function over the interval [a,b] is:

`m=(f(b)-f(a))/(b-a)`

The rate of change of the given function over the interval
`1\leq x\leq 3` is:

`m=(f(3)-f(1))/(3-1)`

From the given table, it is clear that the value of the function is 4 at
`x=1` and 16 at
`x=3`.

`m=(16-4)/(2)`

`m=(12)/(2)`

`m=6`

Therefore, the rate of change of the given function over the interval
`1\leq x\leq 3` is 6.