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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$ and $b = 9$.

Step2: Find $f(0)$ and $f(9)$ from the graph

From the graph, when $x = 0$, $f(0)=10$. When $x = 9$, $f(9)=- 30$.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 9$, $f(0)=10$ and $f(9)=-30$ into the formula: $\frac{f(9)-f(0)}{9 - 0}=\frac{-30 - 10}{9}=\frac{-40}{9}=-\frac{40}{9}$.

Answer:

$-\frac{40}{9}$