Question

problem 8: spiral review
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

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

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

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

Explanation:

Step1: Identify key function values

From the graph:

• $g(-2) = 6$
• $g(1) = 5$
• $g(5) = 2$
• $g(8) = 7$
• $g(15) = 0$

Step2: Calculate rate for $r=-2$ to $r=1$

Use average rate formula $\frac{g(r_2)-g(r_1)}{r_2-r_1}$
$\frac{g(1)-g(-2)}{1-(-2)} = \frac{5-6}{1+2} = \frac{-1}{3}$

Step3: Calculate rate for $r=-2$ to $r=5$

Apply average rate formula
$\frac{g(5)-g(-2)}{5-(-2)} = \frac{2-6}{5+2} = \frac{-4}{7}$

Step4: Calculate rate for $r=-2$ to $r=8$

Apply average rate formula
$\frac{g(8)-g(-2)}{8-(-2)} = \frac{7-6}{8+2} = \frac{1}{10}$

Answer:

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