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The problem asks to find the average rate of change of the function \( f \) over the interval \( 1 \leq x \leq 7 \).

To compute the **average rate of change** of a function \( f(x) \) over the interval \([a, b]\), we use the formula:

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

Here, the interval is from \( x = 1 \) to \( x = 7 \), so:

- \( a = 1 \)
- \( b = 7 \)
- \( f(1) \) is the function value at \( x = 1 \), and \( f(7) \) is the function value at \( x = 7 \).

From the graph:

- \( f(1) = 2 \) (y-coordinate when \( x = 1 \))
- \( f(7) = 2 \) (y-coordinate when \( x = 7 \))

Now applying the formula:

\[
\frac{f(7) - f(1)}{7 - 1} = \frac{2 - 2}{6} = \frac{0}{6} = 0
\]

Therefore, the average rate of change is **0**.

The correct answer is **B: 0**.

Would you like more details or have any further questions? Here are five related questions to deepen your understanding:

1. How would you calculate the average rate of change if the interval was \(1 \leq x \leq 5\)?
2. What is the geometric interpretation of the average rate of change being zero?
3. How does the slope of each individual segment relate to the overall average rate of change?
4. How could you calculate the instantaneous rate of change at \( x = 4 \)?
5. If the interval was extended to include more points, how might that affect the average rate of change?

**Tip:** The average rate of change over an interval is equivalent to the slope of the secant line connecting the two endpoints of the function on that interval.

The graph of the function f, shown above, consists of three line segments. What is the average rate of change of f over the interval 1 <= x <= 7?

Learn how to find the average rate of change of a function over the interval 1 <= x <= 7, where the function consists of three linear segments. Understand the key formula and the relationship between the secant line and the function's rate of change.

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