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Question
x y
2 7
3 10.5
4 14
5 17.5
6 21
Which function has a greater rate of change than the function represented in the table.
Responses
A y = 4xy = 4x
B y = x + 2y = x + 2
C y = 2x + 3y = 2x + 3
D y = 3x + 4
To determine which function has a greater rate of change than the function represented in the table, we need to compare the slopes of the functions.
The slope of a linear function can be found by calculating the change in y divided by the change in x.
In the given table, the change in x is always 1 (since the x-values increase by 1 each time) and the corresponding change in y is shown as follows:
Change in y for x=2: 7 - 0 = 7
Change in y for x=3: 10.5 - 7 = 3.5
Change in y for x=4: 14 - 10.5 = 3.5
Change in y for x=5: 17.5 - 14 = 3.5
Change in y for x=6: 21 - 17.5 = 3.5
Since the change in y is constant at 3.5 for the given function, any function with a greater slope (rate of change) would need to have a change in y that is greater than 3.5 for a change in x of 1.
Now let's analyze the given options:
A) y = 4x
The slope of this function is 4, so the change in y for a change in x of 1 would be 4. Since 4 is greater than 3.5, option A has a greater rate of change.
B) y = x + 2
The slope of this function is 1, which means the change in y for a change in x of 1 would be 1. Since 1 is smaller than 3.5, option B does not have a greater rate of change.
C) y = 2x + 3
The slope of this function is 2, so the change in y for a change in x of 1 would be 2. Since 2 is smaller than 3.5, option C does not have a greater rate of change.
D) y = 3x + 4
The slope of this function is 3, so the change in y for a change in x of 1 would be 3. Since 3 is smaller than 3.5, option D does not have a greater rate of change.
Therefore, the correct answer is A) y = 4x.