Three functions are shown.
The graph titled function A has a line passing through the points (0, 2) and (6, 7).
Function B
x 0 2 4 6
y 2.50 4.03 5.56 7.09
Function C
Drag the functions to order them from LEAST to GREATEST rate of change.
The rate of change of a function can be determined by calculating the slope of the line or by finding the difference in y-values divided by the difference in x-values for each pair of points.
For Function A, the slope can be calculated as follows:
Slope = (change in y) / (change in x)
Slope = (7 - 2) / (6 - 0)
Slope = 5 / 6
For Function B, the rate of change can be calculated for each pair of points:
Rate of change between (0, 2.50) and (2, 4.03):
Rate of change = (4.03 - 2.50) / (2 - 0)
Rate of change = 1.53 / 2
Rate of change = 0.765
Rate of change between (2, 4.03) and (4, 5.56):
Rate of change = (5.56 - 4.03) / (4 - 2)
Rate of change = 1.53 / 2
Rate of change = 0.765
Rate of change between (4, 5.56) and (6, 7.09):
Rate of change = (7.09 - 5.56) / (6 - 4)
Rate of change = 1.53 / 2
Rate of change = 0.765
For Function C, the rate of change can be calculated for each pair of points:
Rate of change between (0, 4) and (2, 6):
Rate of change = (6 - 4) / (2 - 0)
Rate of change = 2 / 2
Rate of change = 1
Rate of change between (2, 6) and (4, 8):
Rate of change = (8 - 6) / (4 - 2)
Rate of change = 2 / 2
Rate of change = 1
Rate of change between (4, 8) and (6, 10):
Rate of change = (10 - 8) / (6 - 4)
Rate of change = 2 / 2
Rate of change = 1
From the calculations, we can determine that the order of the functions from LEAST to GREATEST rate of change is:
Function A, Function B, Function C