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 $x=-2$, $y = f(-2)=-3$. When $x = 4$, $y=f(4)=6$.

Step3: Calculate the average rate of change

Substitute $a=-2$, $b = 4$, $f(-2)=-3$ and $f(4)=6$ into the formula: $\frac{f(4)-f(-2)}{4-(-2)}=\frac{6-(-3)}{4 + 2}$.
Simplify the numerator and denominator: $\frac{6 + 3}{6}=\frac{9}{6}=\frac{3}{2}$.

Answer:

$\frac{3}{2}$