Question

use the graph to answer the question. what is the average rate of change from ( x = 0 ) to ( x = 18 )? ( -\frac{18}{5} ) ( -\frac{5}{18} ) ( \frac{5}{18} ) ( \frac{18}{5} )

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x = a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\) and \(b=18\).

Step2: Find the values of \(f(a)\) and \(f(b)\)

From the graph, when \(x = 0\), \(y=f(0)=10\) (the \(y\) - intercept). When \(x = 18\), \(y = f(18)=5\).

Step3: Substitute into the formula

Substitute \(a = 0\), \(b = 18\), \(f(a)=10\), and \(f(b)=5\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{5 - 10}{18-0}=\frac{- 5}{18}\).

Answer:

\(-\frac{5}{18}\) (the second option)