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 = 3 to x = 5. 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 = 3 to x = 5. 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, $a = 3$ and $b = 5$.

Step2: Find $f(3)$ and $f(5)$ from the graph

From the graph, when $x = 3$, $f(3)=-2$. When $x = 5$, $f(5)=-2$.

Step3: Calculate the average rate of change

Substitute $f(3)=-2$, $f(5)=-2$, $a = 3$, and $b = 5$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(5)-f(3)}{5 - 3}=\frac{-2-(-2)}{2}=\frac{-2 + 2}{2}=0$.

Answer:

$0$