Question

use the graph of f to evaluate the following: the average rate of change of f from 2 to 4 = question help: video submit question

Explanation:

Answer:

To find the average rate of change of \( f \) from \( x = 2 \) to \( x = 4 \), we use the formula for average rate of change:

\[
\text{Average rate of change} = \frac{f(4) - f(2)}{4 - 2}
\]

From the graph:

• At \( x = 2 \), \( f(2) = 0 \) (the graph touches the x - axis at \( x = 2 \)).
• At \( x = 4 \), \( f(4) = 5 \) (the graph reaches a y - value of 5 at \( x = 4 \)).

Substitute these values into the formula:

\[
\text{Average rate of change} = \frac{5 - 0}{4 - 2}=\frac{5}{2} = 2.5
\]

So the average rate of change of \( f \) from 2 to 4 is \(\frac{5}{2}\) (or 2.5).