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: Identify $f(6)$ and $f(7)$

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

Step2: Apply average rate formula

The formula for average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=6$, $b=7$, $f(6)=0$, $f(7)=4$:
$\frac{f(7)-f(6)}{7-6}=\frac{4-0}{7-6}$

Step3: Calculate the result

$\frac{4-0}{7-6}=\frac{4}{1}=4$

Answer:

4