Question

use the graph of f to evaluate the following:
the average rate of change of f from 1 to 5 =
question help: video

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, $a = 1$ and $b = 5$.

Step2: Find $f(1)$ and $f(5)$ from the graph

From the graph, when $x = 1$, $f(1)=5$; when $x = 5$, $f(5)=2$.

Step3: Calculate the average rate of change

Substitute $a = 1$, $b = 5$, $f(1)=5$, and $f(5)=2$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(5)-f(1)}{5 - 1}=\frac{2 - 5}{4}=\frac{-3}{4}=-\frac{3}{4}$.

Answer:

$-\frac{3}{4}$