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:

Identify the coordinates from the graph

We need to find the average rate of change of the function \(f(x)\) from \(x = 0\) to \(x = 18\).
First, let's locate the points on the graph corresponding to these inputs:

• At \(x = 0\), the graph starts on the y-axis at \(y = 10\). So, the first point is \((0, 10)\).
• At \(x = 18\), we look at the grid. The horizontal axis has major grid lines every 2 units. At \(x = 18\), the corresponding point on the graph is at \(y = 5\). So, the second point is \((18, 5)\).

Apply the average rate of change formula

The average rate of change of a function \(f(x)\) over the interval \([a, b]\) is given by the formula:

$$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$

Substituting our values \(a = 0\) and \(b = 18\):

$$ \text{Average Rate of Change} = \frac{f(18) - f(0)}{18 - 0} $$

Calculate the final value

Substitute the function values \(f(0) = 10\) and \(f(18) = 5\) into the formula:

$$ \text{Average Rate of Change} = \frac{5 - 10}{18 - 0} = \frac{-5}{18} = -\frac{5}{18} $$

This matches the second option.

Answer:

• (A) \(-\frac{18}{5}\)
• (B) \(-\frac{5}{18}\) (Correct answer)
• (C) \(\frac{5}{18}\)
• (D) \(\frac{18}{5}\)