To calculate the average rate of change of a function \( f(x) \) over the interval \([-1, 1]\), we use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = -1 \) and \( b = 1 \).
To compute this, you need the values of the function at the endpoints of the interval, \( f(-1) \) and \( f(1) \). You can usually find these values by examining the function's graph at \( x = -1 \) and \( x = 1 \).
- Find \( f(-1) \): Locate the point on the graph corresponding to \( x = -1 \).
- Find \( f(1) \): Locate the point on the graph corresponding to \( x = 1 \).
Assuming we have those values, denote them as:
- \( f(-1) = y_1 \)
- \( f(1) = y_2 \)
Next, substitute these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{y_2 - y_1}{1 - (-1)} = \frac{y_2 - y_1}{2} \]
Finally, replace \( y_1 \) and \( y_2 \) with their actual values from the graph to find the answer.
Since you haven't provided the graphical data or values, I cannot compute the precise average rate of change. Please refer to the graph to find the values of \( f(-1) \) and \( f(1) \), perform the calculation, and you will have your answer.
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