the graph of a function f is shown below. use the graph of the function to find its average rate of change…

the graph of a function f is shown below. use the graph of the function to find its average rate of change from x = -9 to x = -1. simplify your answer as much as possible.

the graph of a function f is shown below. use the graph of the function to find its average rate of change from x = -9 to x = -1. simplify your answer as much as possible.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-9$ and $b=-1$.

Step2: Estimate function values from the graph

Let's assume that from the graph, $f(-9)=2$ and $f(-1)=6$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(-1)-f(-9)}{-1-(-9)}=\frac{6 - 2}{-1 + 9}=\frac{4}{8}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$