To determine the rate of change of each function, we can look at the slope for the linear functions and analyze the data for function B.
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Function A: The points (0, 2) and (6, 7) provide us the slope. \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.833 \]
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Function B: We can calculate the change in \( y \) over the change in \( x \) between the values given:
- From \( (0, 2.50) \) to \( (2, 4.03) \): \[ \text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} = 0.765 \]
- From \( (2, 4.03) \) to \( (4, 5.56) \): \[ \text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} = 0.765 \]
- From \( (4, 5.56) \) to \( (6, 7.09) \): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765 \] The slope for function B is approximately constant at about \( 0.765 \).
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Function C: The equation \( y = 1.3x + 1 \) has a slope of \( 1.3 \).
Now, comparing the rates of change:
- Function B: \( \approx 0.765 \)
- Function A: \( \approx 0.833 \)
- Function C: \( 1.3 \)
Ordering from least to greatest rate of change:
- Function B (0.765)
- Function A (0.833)
- Function C (1.3)
So the order is: Function B, Function A, Function C.
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