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To calculate the average rate of change over the interval \(-1 \leq x \leq 1\), we can use the formula for the average rate of change, which is given by:

\[
\frac{f(b) - f(a)}{b - a}
\]

where \(a\) and \(b\) are the endpoints of the interval, and \(f(a)\) and \(f(b)\) are the corresponding function values at these points.

Looking at the graph:

1. For \(x = -1\), the function value \(f(-1)\) appears to be \(-4\).
2. For \(x = 1\), the function value \(f(1)\) appears to be \(4\).

Using these points:
\[
\text{Average rate of change} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4 - (-4)}{1 + 1} = \frac{4 + 4}{2} = \frac{8}{2} = 4
\]

Thus, the average rate of change over the interval \([-1, 1]\) is \(4\).

Would you like further explanation on this? Here are some related questions:

1. How does the average rate of change relate to the slope of a line?
2. What does it mean if the average rate of change is zero?
3. How do you interpret a negative average rate of change?
4. Can you find the average rate of change over a different interval?
5. How would the calculation change if the points were not on a straight line?

**Tip:** For linear functions, the average rate of change over any interval is the same and equals the slope of the line.

Calculate the average rate of change over the interval \(-1 \leq x \leq 1\).

Learn how to calculate the average rate of change for a linear function over the interval -1 ≤ x ≤ 1. This problem covers key mathematical concepts like the slope of a line and average rate of change, suitable for students in Grades 8-10.

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