To find the rate of change of the function represented by the table, we can calculate the change in \( y \) divided by the change in \( x \) (also known as the slope of the line connecting the points).
We'll calculate the change in \( y \) and the change in \( x \) between any two points. Let's use the points \( (1, -8.5) \) and \( (4, -1) \):
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Calculate \( \Delta y \): \[ \Delta y = y_2 - y_1 = -1 - (-8.5) = -1 + 8.5 = 7.5 \]
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Calculate \( \Delta x \): \[ \Delta x = x_2 - x_1 = 4 - 1 = 3 \]
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Now, calculate the rate of change (slope): \[ \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{7.5}{3} = 2.5 \]
The rate of change of the function is \( 2.5 \). Therefore, the answer is:
2.5