To order the functions by their rate of change, we need to calculate the rate of change (or slope) for each function if possible.
Function A: The line passes through the points (0, 2) and (6, 7). The slope \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.83 \]
Function B: To find the average rate of change for Function B based on the provided data, we need to compare the values at the endpoints (0 and 6).
The values at these points are:
- At \( x = 0 \), \( y = 2.50 \)
- At \( x = 6 \), \( y = 7.09 \)
Using the slope formula:
\[ m = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765 \]
Function C: Without any specific data points given for Function C, we can't directly calculate the rate of change. If we know it to be constant, increasing, or decreasing, or if given endpoints, we could derive a value.
Comparing the Rates of Change:
Now that we have calculated the rates of change for the functions we can compare them:
- Function A: approximately \(0.83\)
- Function B: approximately \(0.765\)
Since Function C does not have a specified rate of change, we will assume that the values provided for Functions A and B will help with ordering.
Assuming that Function C's rate of change is less than the calculated rates above (based on a typical assumption of behavior in graphing problems where data isn't provided or is simply undefined), we can tentatively place it at the base tier until proven otherwise.
Order from Least to Greatest Rate of Change:
- Function C (assumed to be the least)
- Function B (approximately \(0.765\))
- Function A (approximately \(0.83\))
Thus the final order from least to greatest rate of change would be:
- Function C
- Function B
- Function A