question\ngiven the function defined in the table below, find the average rate of change, in simplest form…

question\ngiven 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 ).\nanswer

question\ngiven 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 ).\nanswer

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)