Question

here is the graph of $g(r)$.
determine the average rate of change for each interval in the graph of $g(r)$.

interval

average rate of change

----

----

$r=-2$ to $r=1$

$r=-2$ to $r=5$

$r=-2$ to $r=8$

$\frac{1}{10}$

Explanation:

Step1: Recall average rate of change formula

The average rate of change of $g(r)$ from $r=a$ to $r=b$ is $\frac{g(b)-g(a)}{b-a}$.

Step2: Find $g(-2), g(1), g(5), g(8)$

From the graph:
$g(-2)=6$, $g(1)=5$, $g(5)=2$, $g(8)=7$

Step3: Calculate for $r=-2$ to $r=1$

Substitute values into the formula:
$\frac{g(1)-g(-2)}{1-(-2)}=\frac{5-6}{1+2}=\frac{-1}{3}$

Step4: Calculate for $r=-2$ to $r=5$

Substitute values into the formula:
$\frac{g(5)-g(-2)}{5-(-2)}=\frac{2-6}{5+2}=\frac{-4}{7}$

Answer:

Interval	Average Rate of Change
$r=-2$ to $r=5$	$\frac{-4}{7}$
$r=-2$ to $r=8$	$\frac{1}{10}$