To find the average rate of change of the function \( f(x) = -10x \) over the interval \([-1, 3]\), we use the formula for the average rate of change:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = -1 \) and \( b = 3 \).
First, we need to calculate \( f(-1) \) and \( f(3) \):
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Calculate \( f(-1) \): \[ f(-1) = -10(-1) = 10 \]
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Calculate \( f(3) \): \[ f(3) = -10(3) = -30 \]
Now we can substitute these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{f(3) - f(-1)}{3 - (-1)} = \frac{-30 - 10}{3 + 1} = \frac{-40}{4} = -10 \]
Therefore, the average rate of change of \( f(x) = -10x \) over the interval \([-1, 3]\) is \(\boxed{-10}\).