Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -8 leq x leq -7 )?

Explanation:

Step1: Identify $f(-8)$ and $f(-7)$

From the graph, $f(-8)=16$, $f(-7)=9$

Step2: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=-8$, $b=-7$:
$\frac{f(-7)-f(-8)}{-7-(-8)} = \frac{9-16}{-7+8}$

Step3: Calculate the value

$\frac{9-16}{-7+8} = \frac{-7}{1} = -7$

Answer:

$-7$