To determine the rate of change for each function, we need to analyze their equations or slopes.
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Function A: This function is a linear function that passes through the points (0, 2) and (6, 7). To find the slope (rate of change), we use the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.833 \]
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Function B: Function B does not have an explicit equation accessible, but we can estimate the slope by looking at the provided values:
- From (0, 2.50) to (6, 7.09): \[ \text{slope} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765 \] This is lower than the slope of Function A.
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Function C: This function is given as \(y = 1.3x + 1\). The slope of this linear function is clearly \(1.3\).
Now, we can compare the rates of change:
- Function A: \( \approx 0.833 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)
Ordering these from least to greatest rate of change, we have:
- Function B (approx. 0.765)
- Function A (approx. 0.833)
- Function C (1.3)
So, the final order from least to greatest rate of change is: Function B, Function A, Function C.