Two functions, function A and function B, are shown below:
Function A
x y
7 14
8 16
9 18
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.
Based on the information given, we can determine the rate of change of function A by comparing the changes in the y-values for each change in the x-values. In this case, for each increase in x by 1, y increases by 2. Therefore, the rate of change of function A is 2.
For function B, we can determine the rate of change by looking at the slope of the line that connects the given points. The line passes through the points (2,4), (3,6), and (4,8). By calculating the slope using the formula (change in y)/(change in x), we can see that the rate of change of function B is also 2.
Therefore, the correct answer is:
The rate of change of both functions is 2.