Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-7 \leq x \leq -2$?

Explanation:

Step1: Identify $f(-7)$ and $f(-2)$

From the graph: $f(-7) = 0$, $f(-2) = 28$

Step2: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Here $a=-7$, $b=-2$.
$\text{Average rate} = \frac{f(-2)-f(-7)}{-2 - (-7)} = \frac{28 - 0}{5}$

Step3: Calculate the result

$\frac{28}{5} = 5.6$

Answer:

$5.6$ or $\frac{28}{5}$