Two functions, function A and function B, are shown below:
Function A
x y
7 21
8 24
9 27
Function B
The first quadrant of a coordinate grid is shown from 0 to positive 10 on both axes at intervals of 1. The title is Function B. Only the even numbers are shown on the scale. A line is drawn by connecting the points on ordered pairs 2, 4 and 3, 6 and 4, 8.
Which statement best compares the rate of change of the two functions? (1 point)
The rate of change of both functions is 2.
The rate of change of both functions is 3.
The rate of change of function A is greater than the rate of change of function B.
The rate of change of function B is greater than the rate of change of function A.
To compare the rate of change of the functions, we can look at the change in the y-value (output) for each unit increase in the x-value (input).
For function A:
When x increases from 7 to 8, y increases from 21 to 24.
When x increases from 8 to 9, y increases from 24 to 27.
So the rate of change for function A is 3, meaning that for each unit increase in x, y increases by 3.
For function B:
If we look at the line connecting the points (2, 4), (3, 6), and (4, 8), we can see that for each unit increase in x, y increases by 2.
Therefore, the rate of change of function B is 2.
The statement "The rate of change of function A is greater than the rate of change of function B" is correct.