Question

use the graph of ( f(x) ) to evaluate the following: the average rate of change of ( f ) from ( x = 0 ) to ( x = 5 ) is give your answer as an integer or reduced fraction.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function \( f(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{f(b) - f(a)}{b - a} \).

Step2: Identify \( f(0) \) and \( f(5) \) from the graph

From the graph, when \( x = 0 \), \( f(0) = 3 \). When \( x = 5 \), \( f(5) = 1 \).

Step3: Substitute into the formula

Substitute \( a = 0 \), \( b = 5 \), \( f(0) = 3 \), and \( f(5) = 1 \) into the formula:
\[
\frac{f(5) - f(0)}{5 - 0} = \frac{1 - 3}{5 - 0} = \frac{-2}{5}
\]

Answer:

\( -\frac{2}{5} \)