Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 3leq xleq 5 ).

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, \(a = 3\) and \(b = 5\).

Step2: Identify \(f(a)\) and \(f(b)\) from the table

When \(x=a = 3\), \(f(3)=22\); when \(x = b=5\), \(f(5)=34\).

Step3: Substitute values into the formula

Substitute into \(\frac{f(b)-f(a)}{b - a}\), we get \(\frac{34 - 22}{5-3}\).

Step4: Simplify the expression

First, calculate the numerator: \(34−22 = 12\). Then calculate the denominator: \(5 - 3=2\). So \(\frac{12}{2}=6\).

Answer:

\(6\)