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To find the average rate of change of the function \( f(x) \) on the interval \([-6, 4]\), we use the formula:

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

where \( a = -6 \) and \( b = 4 \). From the graph, we need to find the values of \( f(-6) \) and \( f(4) \).

1. From the graph, at \( x = -6 \), the corresponding value of \( f(-6) \) is approximately 50.
2. At \( x = 4 \), the value of \( f(4) \) is approximately \(-40\).

Now applying the formula:

\[
\text{Average rate of change} = \frac{f(4) - f(-6)}{4 - (-6)} = \frac{-40 - 50}{4 - (-6)} = \frac{-90}{10} = -9
\]

Thus, the average rate of change of \( f(x) \) on the interval \([-6, 4]\) is \( -9 \).

Would you like further details or explanations on this? Here are some related questions to explore:

1. How is the average rate of change different from the instantaneous rate of change?
2. What is the significance of a negative average rate of change?
3. How can you estimate the slope of a curve at a specific point from its graph?
4. What role does the secant line play in calculating average rate of change?
5. How can you use the average rate of change to determine the behavior of a function?

**Tip:** When interpreting a graph, make sure to identify key points precisely, as small errors can impact the result significantly.

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 ≤ 4?

Learn how to calculate the average rate of change of the function f(x) on the interval [-6, 4]. This problem involves interpreting a graph, applying the formula for average rate of change, and understanding the significance of the slope of the secant line. Suitable for students in Grades 10-12.

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