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To find the average rate of change of the function \( f(x) \) on the interval \( 6 \leq x \leq 7 \), we can use the following formula for the average rate of change of a function over an interval:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 6 \) and \( b = 7 \).

### Step 1: Identify \( f(6) \) and \( f(7) \)
Looking at the graph:
- At \( x = 6 \), the function \( f(6) \) appears to be approximately \( 4 \).
- At \( x = 7 \), the function \( f(7) \) appears to be approximately \( 0 \).

### Step 2: Apply the formula
Substituting into the formula:
\[
\text{Average Rate of Change} = \frac{f(7) - f(6)}{7 - 6} = \frac{0 - 4}{7 - 6} = \frac{-4}{1} = -4
\]

### Final Answer:
The average rate of change of the function \( f(x) \) on the interval \( 6 \leq x \leq 7 \) is \( -4 \).

Would you like any further clarification or details?

Here are some related questions for deeper understanding:
1. How is the average rate of change different from the instantaneous rate of change?
2. What does a negative rate of change signify in the context of a graph?
3. How would the average rate of change be different for a different interval, say from \( 5 \leq x \leq 6 \)?
4. Can you explain how to estimate values like \( f(6) \) and \( f(7) \) from the graph more precisely?
5. How does the graph's shape influence the average rate of change?

**Tip:** The average rate of change can be thought of as the slope of the secant line connecting two points on a graph.

The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 6 ≤ x ≤ 7?

This problem explains how to find the average rate of change of the function f(x) on the interval 6 ≤ x ≤ 7 using graph interpretation and algebraic concepts. A step-by-step solution shows how to apply the rate of change formula to get the result of -4.

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