Question

score: 0 of 1 point
use the graph of f to evaluate the following:
the average rate of change of f from 4 to 5 is
a 4

Explanation:

Step1: Recall the formula for average rate of change

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, \(a = 4\) and \(b=5\).

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

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

Step3: Substitute into the formula

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

Answer:

\(-4\)