The formula to calculate the average rate of change is given to be:
[tex]AROC=\frac{f(b)-f(a)}{b-a}[/tex]
where a and b are the values of x and f(a) and f(b) are the corresponding values of y.
The image below shows the values of f(a) and f(b) when a and b are 1 and 4 respectively:
Therefore, we have the following parameters:
[tex]\begin{gathered} a=1 \\ b=4 \\ f(a)=5 \\ f(b)=3.5 \end{gathered}[/tex]
Therefore, we can calculate the average rate of change is calculated to be:
[tex]\begin{gathered} AROC=\frac{3.5-5}{4-1}=\frac{-1.5}{3} \\ AROC=-0.5 \end{gathered}[/tex]
The average rate of change is -0.5.
