the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 3$ and $b = 6$.

Step2: Estimate function values from the graph

From the graph, when $x = 3$, assume $f(3)=4$ (by looking at the $y$ - value of the graph at $x = 3$). When $x = 6$, assume $f(6)= - 2$ (by looking at the $y$ - value of the graph at $x = 6$).

Step3: Calculate the average rate of change

Substitute $a = 3$, $b = 6$, $f(3)=4$ and $f(6)=-2$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(6)-f(3)}{6 - 3}=\frac{-2 - 4}{3}=\frac{-6}{3}=-2$.

Answer:

$-2$