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 + 4y = 3x + 4

Answer 1

To determine which function has a greater rate of change, we can examine the difference in y-values for a one-unit increase in x. Let's calculate the rate of change for each function:

A: y = 4x
Using the given values in the table, we can determine the rate of change by finding the difference in y-values for a one-unit increase in x:
(3, 10.5) - (2, 7) = 10.5 - 7 = 3.5
The rate of change for this function is 3.5.

B: y = x + 2
(3, 10.5) - (2, 7) = 10.5 - 7 = 3.5
The rate of change for this function is 3.5.

C: y = 2x + 3
(3, 10.5) - (2, 7) = 10.5 - 7 = 3.5
The rate of change for this function is also 3.5.

D: y = 3x + 4
(3, 10.5) - (2, 7) = 10.5 - 7 = 3.5
The rate of change for this function is 3.5.

Since all the functions have the same rate of change of 3.5, none of them has a greater rate of change than the function represented in the table.