Determine which function has the greater rate of change in problems 1-3.
x -1 0 1 2
y 0 1 2 3
A. The rates of change are equal.
B. The graph has a greater rate of change.
C. The table has greater rate of change.
D. None of the above.
A. The rates of change are equal because for every 1 unit increase in x, y also increases by 1 unit.
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Is there anything I can assist you with?
To determine which function has the greater rate of change, we need to compare the rates of change for both the graph and the table.
Let's calculate the rate of change for the graph and the table:
For the graph, we can see that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1. This means that the rate of change for the graph is 1.
For the table, we can calculate the rate of change by finding the differences between consecutive y-values and the corresponding x-values. Starting from the first row:
x-1: y(0) - y(-1) = 1 - 0 = 1
x-0: y(1) - y(0) = 2 - 1 = 1
x-1: y(2) - y(1) = 3 - 2 = 1
We can see that in the table, for every increase of 1 in the x-coordinate, the y-coordinate also increases by 1. Therefore, the rate of change for the table is also 1.
Since the rates of change for both the graph and the table are equal, the correct answer is:
A. The rates of change are equal.
Therefore, option A is the correct answer.