Question

what is the average rate of change for the given graph over the interval -2 ≤ x ≤ 4

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 4$.

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

From the graph, when $x=-2$, $y = - 2$ (i.e., $f(-2)=-2$). When $x = 4$, $y=6$ (i.e., $f(4)=6$).

Step3: Calculate the average rate of change

Substitute $a=-2$, $b = 4$, $f(-2)=-2$ and $f(4)=6$ into the formula: $\frac{f(4)-f(-2)}{4-(-2)}=\frac{6-(-2)}{4 + 2}=\frac{6 + 2}{6}=\frac{8}{6}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$