Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 \leq x \leq 1$?

Explanation:

Step1: Identify $f(-6)$ and $f(1)$

From the graph: $f(-6) = -50$, $f(1) = 10$

Step2: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Here $a=-6$, $b=1$.
$\text{Average rate of change} = \frac{f(1)-f(-6)}{1-(-6)} = \frac{10 - (-50)}{1 + 6} = \frac{60}{7}$

Answer:

$\frac{60}{7}$