To determine the rate of change for each of the functions, we can analyze each one.
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Function A: The line passing through the points (0, 2) and (6, 7) has a slope (rate of change) given by: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.83 \]
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Function B: To find the rate of change for Function B, we can calculate the average rate of change between the given points:
- Between (0, 2.50) and (2, 4.03): \[ \text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} \approx 0.765 \]
- Between (2, 4.03) and (4, 5.56): \[ \text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} \approx 0.765 \]
- Between (4, 5.56) and (6, 7.09): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} \approx 0.765 \]
- The average rate of change for Function B appears to be approximately 0.765.
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Function C: The function is expressed as \( y = 1.3x + 1 \), so the rate of change (slope) is clearly 1.3.
Now we can order the functions based on their rates of change:
- Function A: \( \approx 0.83 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)
Ordering from LEAST to GREATEST rate of change, we have:
- Function B (≈ 0.765)
- Function A (≈ 0.83)
- Function C (1.3)
So, the correct order is:
Least ----------------------------------------> Greatest Function B Function A Function C