Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $6 \leq x \leq 7$?

Explanation:

Step1: Recall average rate of change formula

The average rate of change of $f(x)$ on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify $f(6)$ and $f(7)$ from graph

From the graph, $f(6)=4$, $f(7)=0$.

Step3: Substitute values into formula

$$\frac{f(7)-f(6)}{7-6}=\frac{0-4}{7-6}$$

Step4: Calculate the result

$$\frac{-4}{1}=-4$$

Answer:

$-4$