Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
The average rate of change of a function [tex]f[/tex] on the interval [tex][a,b][/tex] is [tex]\frac{f(b)-f(a)}{b-a}[/tex].
So the average rate of change of our function [tex]f[/tex] here on the interval [tex][-4,5][/tex] is [tex]\frac{f(5)-f(-4)}{5-(-4)}=\frac{f(5)-f(-4)}{9}[/tex].
We need to figure out both [tex]f(5)[/tex] and [tex]f(-4)[/tex].
[tex]f(5)[/tex] corresponds to the value in the 2nd column when the first column value is [tex]5[/tex]. This number is 4.
[tex]f(5)=4[/tex].
[tex]f(-4)[/tex] corresponds to the value in the 2nd column when the first column value is [tex]-4[/tex]. This number is 2.
Let's go back to computing the average rate of change of [tex]f[/tex] on [tex][-4,5][/tex]:
[tex]\frac{4-2}{9}=\frac{2}{9}[/tex].
The answer is [tex]\frac{2}{9}[/tex].
