Which table shows a nonlinear relationship between x and y?

Answer options with 4 options
A. x 1 4 5 7 y 12 9 8 6
B. x 2 4 8 16 y 4 4 4 4
C. x 1 2 3 4 y 5 7 9 11
D. x 2 3 4 5 y 3 4 6 9

1 answer

To determine which table shows a nonlinear relationship between x and y, we can analyze the given options:

A.

x: 1, 4, 5, 7  
y: 12, 9, 8, 6

This relationship decreases as x increases, but not in a consistent linear fashion.

B.

x: 2, 4, 8, 16  
y: 4, 4, 4, 4

This relationship is constant; hence it is linear.

C.

x: 1, 2, 3, 4  
y: 5, 7, 9, 11

Here, y increases linearly as x increases.

D.

x: 2, 3, 4, 5  
y: 3, 4, 6, 9

The values of y do not increase consistently; the differences between consecutive y values are increasing (1, 2, 3), indicating a nonlinear relationship.

Based on this analysis, the answer is:

D.