Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $2leq xleq8$.

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, \(a = 2\), \(b=8\), \(f(a)=f(2) = 1\), and \(f(b)=f(8)=37\).

Step2: Substitute the values into the formula

Substitute the values into \(\frac{f(b)-f(a)}{b - a}\), we get \(\frac{37 - 1}{8 - 2}\).

Step3: Simplify the expression

First, calculate the numerator \(37-1=36\) and the denominator \(8 - 2=6\). Then \(\frac{36}{6}=6\).

Answer:

\(6\)