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

Explanation:

Step1: Identify the interval and the formula for the average rate of change.

The interval is $[-2, 7]$. The average rate of change of a function $f(x)$ on an interval $[a, b]$ is given by: $$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$ Here, $a = -2$ and $b = 7$.

Step2: Find the function values at the endpoints of the interval from the graph.

From the graph, we find the value of $f(x)$ at $x = -2$ and $x = 7$. When $x = -2$, $f(-2) = 20$. When $x = 7$, $f(7) = 0$.

Step3: Substitute the values into the formula and calculate.

Substitute $a = -2$, $b = 7$, $f(-2) = 20$, and $f(7) = 0$ into the formula: $$ \text{Average Rate of Change} = \frac{f(7) - f(-2)}{7 - (-2)} $$ $$ \text{Average Rate of Change} = \frac{0 - 20}{7 + 2} $$ $$ \text{Average Rate of Change} = \frac{-20}{9} $$

Answer:

$$ -\frac{20}{9} $$