Question

using the function graph shown below, calculate the average rate of change from ( x = 3 ) to ( x = 8 ).

Explanation:

Step1: Determine the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify the values of \(f(a)\) and \(f(b)\) from the graph

When \(a = 3\), from the graph \(f(3)=-4\). When \(b = 8\), from the graph \(f(8)=-8\).

Step3: Substitute the values into the formula

Substitute \(a = 3\), \(b = 8\), \(f(3)=-4\), and \(f(8)=-8\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-8-(-4)}{8 - 3}=\frac{-8 + 4}{5}\).

Step4: Simplify the expression

\(\frac{-8 + 4}{5}=\frac{-4}{5}=-0.8\)

Answer:

\(-0.8\)