To determine the order of the functions from least to greatest rate of change, we can first calculate the slope (rate of change) for each function.
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Function A: Given points (0, 2) and (6, 7): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.833 \]
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Function B: The values provided do not give a clear linear representation, but we can approximate the average rate of change between the points.
- From (0, 2.50) to (6, 7.09): \[ \text{slope} \approx \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765 \]
Alternatively, checking between each interval:
- 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): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765 \]
Overall average slope is aproximadamente the same.
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Function C: Given in the form \(y = 1.3x + 1\), the slope is straightforward: \[ \text{slope} = 1.3 \]
Now we can summarize the slopes:
- Function A: 0.833
- Function B: 0.765 (average approximated)
- Function C: 1.3
Ordering from least to greatest rate of change:
- Function B
- Function A
- Function C
Therefore, the order from least to greatest is:
- Function B
- Function A
- Function C