Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 \leq x \leq -3$?

Explanation:

Step1: Identify $f(-6)$ and $f(-3)$

From the graph: $f(-6)=20$, $f(-3)=7$

Step2: Apply average rate formula

The average rate of change is $\frac{f(b)-f(a)}{b-a}$ for interval $[a,b]$. Here $a=-6$, $b=-3$.
$\text{Average rate} = \frac{f(-3)-f(-6)}{-3-(-6)} = \frac{7-20}{-3+6}$

Step3: Calculate the result

$\frac{7-20}{3} = \frac{-13}{3}$

Answer:

$\boldsymbol{-\frac{13}{3}}$