The average rate of change of a function is given by the following formula.
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 3 and b= 11.
First, evaluate the function when x = 3.
[tex]\begin{gathered} f(x)=2x+7_{} \\ f(3)=2(3)+7=6+7=13 \end{gathered}[/tex]This means f(a) = 13.
Second, evaluate the function when x = 11.
[tex]f(11)=2(11)+7=22+7=29[/tex]This means f(b) = 29.
Once we have all the values we need, we can find the average rate of change using the formula.
[tex]\begin{gathered} r=\frac{f(b)-f(a)}{b-a} \\ r=\frac{29-13}{11-3} \\ r=\frac{16}{8} \\ r=2 \end{gathered}[/tex]