Question

using the function graph shown below, calculate the average rate of change on the interval 4 ≤ x ≤ 7.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 4\) and \(b=7\).

Step2: Find \(f(4)\) and \(f(7)\) from the graph

From the graph, when \(x = 4\), \(f(4)=- 6\); when \(x = 7\), \(f(7)=-7\).

Step3: Substitute into the formula

Substitute \(a = 4\), \(b = 7\), \(f(4)=-6\), and \(f(7)=-7\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-7-(-6)}{7 - 4}=\frac{-7 + 6}{3}=\frac{-1}{3}\).

Answer:

\(-\frac{1}{3}\)