Question

use the graph of f to evaluate the following: the average rate of change of f from 4 to 5 = question help: video message instructor submit question

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \). Here, \( a = 4 \) and \( b = 5 \).

Step2: Find \( f(4) \) and \( f(5) \) from the graph

From the graph, when \( x = 4 \), \( f(4)=2 \); when \( x = 5 \), \( f(5) = 1 \).

Step3: Calculate the average rate of change

Substitute \( a = 4 \), \( b = 5 \), \( f(4)=2 \), and \( f(5)=1 \) into the formula:
\[
\frac{f(5)-f(4)}{5 - 4}=\frac{1 - 2}{1}=\frac{- 1}{1}=-1
\]

Answer:

\(-1\)