Answer
-1
Step-by-step explanation
The average rate of change of function f(x) over the interval a ≤ x ≤ b is calculated as follows:
[tex]avg\text{ rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]where f(b) and f(a) are the function f(x) evaluated at x = b and x = a respectively.
In this case, the function is:
[tex]f(x)=x^2-7x+8[/tex]And the interval is -1 ≤ x ≤ 7. Evaluating f(x) at x = 7 and x = -1:
[tex]\begin{gathered} f(7)=7^2-7\cdot7+8 \\ f(7)=49-49+8 \\ f(7)=8 \\ f(-1)=(-1)^2-7\cdot(-1)+8 \\ f(-1)=1+7+8 \\ f(-1)=16 \end{gathered}[/tex]Then, the average rate of change of this function is:
[tex]\begin{gathered} avg\text{ rate of change }=\frac{f(7)-f(-1)}{7-(-1)} \\ avg\text{ rate of change}=\frac{8-16}{7+1} \\ avg\text{ rate of change}=-1 \end{gathered}[/tex]