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:

$m=\dfrac{f(b)-f(a)}{b-a}$

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

$m=\dfrac{f(3)-f(1)}{3-1}$

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

$m=\dfrac{16-4}{2}$

$m=\dfrac{12}{2}$

$m=6$

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