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
y=1.3x+1
Drag the functions to order them from LEAST to GREATEST rate of change.
The rate of change of a linear function can be determined by finding the slope of the line. The greater the absolute value of the slope, the greater the rate of change.
Comparing the given functions:
Function A:
From the given points (0, 2) and (6, 7), we can find the slope as (change in y)/(change in x) = (7-2)/(6-0) = 5/6.
Function B:
By comparing the values of x and y, we can see that the rate of change is not constant. However, we can calculate the average rate of change between any two consecutive points. For example, between x=0 and x=2, (change in y)/(change in x) = (4.03-2.50)/(2-0) = 1.53/2 = 0.765. Similarly, for x=2 and x=4, the rate of change is (change in y)/(change in x) = (5.56-4.03)/(4-2) = 1.53/2 = 0.765. And finally, for x=4 and x=6, the rate of change is (change in y)/(change in x) = (7.09-5.56)/(6-4) = 1.53/2 = 0.765. Although the rate of change is not exactly constant, it is very close to 0.765 in this case.
Function C:
This function is already in slope-intercept form (y=mx+b), where m represents the slope. The coefficient of x in this equation is 1.3, so the slope is 1.3.
Based on these calculations, we can order the functions from least to greatest rate of change:
Function B (approximate rate of change = 0.765)
Function A (exact rate of change = 5/6 ≈ 0.833)
Function C (exact rate of change = 1.3)
Thus, the correct order is: Function B, Function A, Function C.