Answer:
Average rate of change is 2
Step-by-step explanation:
If a function [tex]f(x)[/tex] is continuous over the interval [tex][a,b][/tex], then the average rate of change over that interval is [tex]\displaystyle \frac{f(b)-f(a)}{b-a}[/tex]:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\displaystyle \frac{f(1)-f(-1)}{1-(-1)}\\\\=\frac{(2(1)-11)-(2(-1)-11)}{1+1}\\ \\=\frac{(2-11)-(-2-11)}{2}\\ \\=\frac{-9-(-13)}{2}\\ \\=\frac{-9+13}{2}\\ \\=\frac{4}{2}\\ \\=2[/tex]
Thus, the average rate of change over the interval [tex][-1,1][/tex] for the function [tex]f(x)=2x-11[/tex] is 2.
