Question

given the graph of $f(x)$ below. determine the average rate of change of $f(x)$ from $x=-3$ to $x = 2$.
give your answer as a simplified fraction if necessary. for example, if you found that $m_{sec}=\frac{2}{3}$, you would enter $\frac{2}{3}$.

provide your answer below:

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$ and $b = 2$.

Step2: Identify function values from graph

From the graph, when $x=-3$, $f(-3)=4$; when $x = 2$, $f(2)=2$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(2)-f(-3)}{2-(-3)}=\frac{0 - 2}{2+3}=\frac{-2}{5}=-\frac{2}{5}$.

Answer:

$-\frac{2}{5}$