Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 0leq xleq 6 ).

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, \(a = 0\), \(b=6\), \(f(a)=f(0) = 9\), and \(f(b)=f(6)=15\).

Step2: Substitute the values into the formula

Substitute the values into the formula \(\frac{f(6)-f(0)}{6 - 0}\). We get \(\frac{15 - 9}{6-0}\).

Step3: Simplify the expression

First, calculate the numerator \(15−9 = 6\) and the denominator \(6 - 0=6\). Then \(\frac{6}{6}=1\).

Answer:

$1$