Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-1 \leq x \leq 2$?

Explanation:

Step1: Identify $f(-1)$ and $f(2)$

From the graph: $f(-1)=10$, $f(2)=-20$

Step2: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=-1$, $b=2$:
$\frac{f(2)-f(-1)}{2-(-1)} = \frac{-20 - 10}{2 + 1}$

Step3: Calculate the result

$\frac{-30}{3} = -10$

Answer:

$-10$