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 formula for 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 result

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

Answer:

$-7$