Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 3leq xleq4 ).

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 3\) and \(b=4\).

Step2: Substitute the values from the table

From the table, \(f(3)=4\) and \(f(4) = 4\). Substitute into the formula: \(\frac{f(4)-f(3)}{4 - 3}=\frac{4 - 4}{4-3}\).

Step3: Simplify the expression

\(\frac{4 - 4}{4-3}=\frac{0}{1}=0\).

Answer:

\(0\)