Question

Watch help video-The function y f(x) is graphed below.What is the average rate of change of thefunction f(x) on the interval—7 < x < -3?100

Answer 1

The formula to calculate the average rate of change of a function f(x) over the interval:

$a\leq x\leq b$

is given to be:

$AROC=\frac{f(b)-f(a)}{b-a}$

From the provided question, we have:

$\begin{gathered} a=-7 \\ b=-3 \end{gathered}$

From the graph, we have:

$\begin{gathered} f(a)=-10 \\ f(b)=30 \end{gathered}$

Therefore, the average rate of change is:

$\begin{gathered} AROC=\frac{30-(-10)}{-3-(-7)}=\frac{30+10}{-3+7}=\frac{40}{4} \\ AROC=10 \end{gathered}$

Therefore, the average rate of change is 10.