Determine which function has the greater rate of change in questions 1−4.
x y
-------
-2 4/7
-1 -0.25
0 0
1 0.25
A) The rates of change are equal.
B) The graph has a greater rate of change.
C) The table has a greater rate of change.
D) None of the above
The rate of change can be determined by finding the difference in y-values (Δy) and dividing it by the difference in x-values (Δx).
For the table:
- Between x=-2 and x=-1: Δy = (-0.25) - (4/7) = -0.8929, Δx = -1 - (-2) = 1, rate of change = -0.8929 / 1 = -0.8929
- Between x=-1 and x=0: Δy = 0 - (-0.25) = 0.25, Δx = 0 - (-1) = 1, rate of change = 0.25 / 1 = 0.25
- Between x=0 and x=1: Δy = 0.25 - 0 = 0.25, Δx = 1 - 0 = 1, rate of change = 0.25 / 1 = 0.25
So, the table has a greater rate of change compared to the graph in questions 1-4. Therefore, the answer is C) The table has a greater rate of change.