Question

Determine which function has the greater rate of change in questions 1−4
x y
-------
-1 0
0 1
1 2
2 3

Answer 1

To determine which function has the greater rate of change, we can look at the differences in y-values for each pair of consecutive x-values.

For the function with the points (-1, 0), (0, 1), (1, 2), and (2, 3):

Between x = -1 and x = 0, y changes from 0 to 1, so the rate of change is 1 - 0 = 1.
Between x = 0 and x = 1, y changes from 1 to 2, so the rate of change is 2 - 1 = 1.
Between x = 1 and x = 2, y changes from 2 to 3, so the rate of change is 3 - 2 = 1.

Therefore, the function has a constant rate of change of 1.

Next, we compare this with a function that changes at different rates:

For the function with the points (-1, 0), (0, 1), (1, -1), and (2, 2):

Between x = -1 and x = 0, y changes from 0 to 1, so the rate of change is 1 - 0 = 1.
Between x = 0 and x = 1, y changes from 1 to -1, so the rate of change is -1 - 1 = -2.
Between x = 1 and x = 2, y changes from -1 to 2, so the rate of change is 2 - (-1) = 3.

Therefore, the second function has varying rates of change, with absolute values of 1, 2, and 3 for consecutive intervals. The second function has a greater rate of change compared to the first function.