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, $a=-9$ and $b = 1$.

Step2: Find $f(-9)$ and $f(1)$ from the graph

From the graph, when $x=-9$, $f(-9)=-12$; when $x = 1$, $f(1)=-6$.

Step3: Calculate the average rate of change

Substitute $a=-9$, $b = 1$, $f(-9)=-12$ and $f(1)=-6$ into the formula: $\frac{f(1)-f(-9)}{1-(-9)}=\frac{-6-(-12)}{1 + 9}=\frac{-6 + 12}{10}=\frac{6}{10}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$