To find the intervals where the average rate of the function \( h(x) = -5x + 8 \) is equal to -30, we can calculate the average rate of the function on the provided intervals.
The average rate of change of a function \( h(x) \) from \( x = a \) to \( x = b \) is given by:
\[ \text{Average Rate} = \frac{h(b) - h(a)}{b - a} \]
Now, let’s compute the average rates for each interval provided:
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Interval \( x = -4 \) to \( x = 4 \): \[ h(-4) = -5(-4) + 8 = 20 + 8 = 28 \] \[ h(4) = -5(4) + 8 = -20 + 8 = -12 \] \[ \text{Average Rate} = \frac{-12 - 28}{4 - (-4)} = \frac{-40}{8} = -5 \]
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Interval \( x = 4 \): This interval is just one point, so the average rate is not defined.
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Interval \( x = 0 \) to \( x = 2 \): \[ h(0) = -5(0) + 8 = 8 \] \[ h(2) = -5(2) + 8 = -10 + 8 = -2 \] \[ \text{Average Rate} = \frac{-2 - 8}{2 - 0} = \frac{-10}{2} = -5 \]
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Interval \( x = 2 \) to \( x = 4 \): \[ h(2) = -5(2) + 8 = -2 \] \[ h(4) = -5(4) + 8 = -12 \] \[ \text{Average Rate} = \frac{-12 - (-2)}{4 - 2} = \frac{-10}{2} = -5 \]
After evaluating all four intervals, the average rate of change for all intervals is -5, which is not equal to or close to -30.
Since none of the computed average rates are close to -30, the answer is that none of the provided intervals result in an average rate of change equal to -30. Therefore, if I must choose one of the provided options strictly, I would choose:
x = -4 to x = 4 (since it's the first option).