To solve this problem, we calculate the average rate of change of $f(x)$ from $x = 2$ to $x = 4$. The formula for the average rate of change is:

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

From the graph:

• At $x = 2$, the value of $f(2) = 1$.
• At $x = 4$, the value of $f(4) = 3$.

Substituting into the formula:

$\text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} = \frac{3 - 1}{4 - 2} = \frac{2}{2} = 1$

Final Answer:

The average rate of change is 1.

Would you like a deeper explanation or more help with interpreting graphs?

Related Questions:

1. What is the average rate of change from $x = 0$ to $x = 2$?
2. How do you find the rate of change if $f(x)$ were nonlinear?
3. Why does the formula for the average rate of change resemble the slope of a line?
4. What does it mean when the average rate of change is negative?
5. How can you visually confirm the rate of change using the graph?

Tip: When working with graphs, always carefully identify the coordinates of the points you're using to avoid errors.