Question

question
given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 2 leq x leq 3 ).
answer

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, \(a = 2\) and \(b=3\).

Step2: Substitute the values into the formula

We know that \(f(2)=28\) and \(f(3)=19\). Substituting these values into the formula \(\frac{f(3)-f(2)}{3 - 2}\), we get \(\frac{19 - 28}{3-2}\).

Step3: Simplify the expression

First, calculate the numerator: \(19-28=-9\), and the denominator \(3 - 2=1\). So, \(\frac{-9}{1}=-9\).

Answer:

\(-9\)