Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq 8$?

Explanation:

Step1: Identify $f(-3)$ and $f(8)$

From the graph: $f(-3) = -100$, $f(8) = 20$

Step2: Recall average rate formula

Average rate of change = $\frac{f(b)-f(a)}{b-a}$ for interval $[a,b]$

Step3: Substitute values into formula

$a=-3$, $b=8$, so:
$\frac{f(8)-f(-3)}{8-(-3)} = \frac{20 - (-100)}{8 + 3}$

Step4: Calculate numerator and denominator

$\frac{20 + 100}{11} = \frac{120}{11}$

Answer:

$\frac{120}{11}$