Question

the graph of a function f is shown below. use the graph of the function to find its average rate of change from x = - 4 to x = 2. simplify your answer as much as possible.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-4$ and $b = 2$.

Step2: Identify $f(-4)$ and $f(2)$ from the graph

From the graph, when $x=-4$, $f(-4)=8$, and when $x = 2$, $f(2)=8$.

Step3: Calculate the average rate of change

Substitute $a=-4$, $b = 2$, $f(-4)=8$, and $f(2)=8$ into the formula: $\frac{f(2)-f(-4)}{2-(-4)}=\frac{8 - 8}{2+4}=\frac{0}{6}=0$.

Answer:

$0$