Determine which function has the greater rate of change in problems 1-3. show your work.
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.
C. The table has a greater rate of change.
To determine the rate of change for each function, we can find the slope between any two points on the graph or table. For the table, we can use the formula:
slope = (change in y) / (change in x)
Using the points (0,1) and (1,2) from the table:
slope = (2-1) / (1-0) = 1
Using the points (1,2) and (2,3) from the table:
slope = (3-2) / (2-1) = 1
So the rate of change for the table is the same for both intervals, and it is equal to 1.
For the graph, we can also find the slope between any two points. Using the points (0,1) and (2,3) from the graph:
slope = (3-1) / (2-0) = 1
So the rate of change for the graph is also 1.
Therefore, the answer is that the rates of change are equal, and the correct choice is A.
To determine which function has the greater rate of change, we need to calculate the difference in y-values (Δy) divided by the difference in x-values (Δx) for each set of points.
For problem 1, the points are (-1, 0) and (0, 1).
Δy = 1 - 0 = 1
Δx = 0 - (-1) = 1
Rate of change = Δy/Δx = 1/1 = 1
For problem 2, the points are (0, 1) and (1, 2).
Δy = 2 - 1 = 1
Δx = 1 - 0 = 1
Rate of change = Δy/Δx = 1/1 = 1
For problem 3, the points are (1, 2) and (2, 3).
Δy = 3 - 2 = 1
Δx = 2 - 1 = 1
Rate of change = Δy/Δx = 1/1 = 1
Since the rates of change for all three problems are equal (1), the correct answer is:
A. The rates of change are equal.
To determine which function has the greater rate of change, we need to examine the given data. The rate of change of a function describes how much the output (y-value) changes for a given change in the input (x-value).
Using the given table:
For data point 1:
x = -1, y = 0
For data point 2:
x = 0, y = 1
For data point 3:
x = 1, y = 2
For data point 4:
x = 2, y = 3
To find the rate of change, we can determine the difference in the y-values and the difference in the x-values for each pair of data points.
For the first pair (points 1 and 2):
Change in y = 1 - 0 = 1
Change in x = 0 - (-1) = 1
For the second pair (points 2 and 3):
Change in y = 2 - 1 = 1
Change in x = 1 - 0 = 1
For the third pair (points 3 and 4):
Change in y = 3 - 2 = 1
Change in x = 2 - 1 = 1
From the calculations, we can see that for all three pairs of data points, the change in y is equal to the change in x. This means that the rates of change are all equal, indicating a constant rate of change throughout the data.
Therefore, the correct answer is option A: The rates of change are equal.