consider the graph of f(x). what is the average rate of change of f(x) from x1 = 4 to x2 = 9? please write…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is given by $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Identify $f(x_1)$ and $f(x_2)$ from the graph

When $x_1 = 4$, from the graph $f(4)=5$. When $x_2 = 9$, from the graph $f(9)=4$.

Step3: Substitute values into the formula

Substitute $x_1 = 4$, $x_2 = 9$, $f(4)=5$ and $f(9)=4$ into the formula: $\frac{f(9)-f(4)}{9 - 4}=\frac{4 - 5}{9 - 4}$.

Step4: Simplify the fraction

$\frac{4 - 5}{9 - 4}=\frac{-1}{5}=-\frac{1}{5}$.

Answer:

$-\frac{1}{5}$