Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 6 ≤ x ≤ 18

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, \(a = 6\), \(b=18\), \(f(a)=f(6) = 40\), and \(f(b)=f(18)=30\).

Step2: Substitute values into the formula

Substitute the values into the formula: \(\frac{f(18)-f(6)}{18 - 6}=\frac{30 - 40}{18-6}\).

Step3: Simplify the expression

Simplify the numerator and denominator: \(\frac{30 - 40}{18-6}=\frac{- 10}{12}=-\frac{5}{6}\).

Answer:

\(-\frac{5}{6}\)