The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.
Step-by-step explanation: We are given to find the rate of change from
x = 1 to x = 2, x = 2 to x = 3 and x = 3 to x = 4.
We know that
The average rate of change between x = a to x = b for a function f(x) is given by
![A_v=\dfrac{f(b)-f(a)}{b-a}.](/tpl/images/0335/9521/5dbb4.png)
For the given function f(x), we have from the graph that
f(1) = 2, f(2) = 4, f(3) = 8 and f(4) = 16.
So, the average rate of change from x = 1 to x = 2 is given by
![A_{v1}=\dfrac{f(2)-f(1)}{2-1}=\dfrac{4-2}{1}=2.](/tpl/images/0335/9521/6378d.png)
The average rate of change from x = 2 to x = 3 is given by
![A_{v2}=\dfrac{f(3)-f(2)}{3-2}=\dfrac{8-4}{1}=4.](/tpl/images/0335/9521/3f020.png)
The average rate of change from x = 3 to x = 4 is given by
![A_{v3}=\dfrac{f(4)-f(3)}{4-3}=\dfrac{16-8}{1}=8.](/tpl/images/0335/9521/07f6f.png)
Thus, the average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.