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 ( 1 leq x leq 7 ).\nanswer\nattempt 1 out of 2\nsubmit answer

question\ngiven the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 1 leq x leq 7 ).\nanswer\nattempt 1 out of 2\nsubmit answer

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 = 1) and (b=7).

Step2: Identify (f(a)) and (f(b))

From the table, when (x = 1), (f(1)=66) (so (f(a)=66)), and when (x = 7), (f(7)=6) (so (f(b)=6)).

Step3: Substitute into the formula

Substitute (a = 1), (b = 7), (f(a)=66), and (f(b)=6) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{6 - 66}{7-1}).

Step4: Simplify the expression

First, calculate the numerator: (6-66=-60). Then calculate the denominator: (7 - 1=6). So (\frac{-60}{6}=-10).

Answer:

(-10)