Question

The table shows a function. Is the function linear or nonlinear?

x y
0 3
6 6
18 12

Answer 1

[AI-generated answer — Bot GPT 3.5]

The function is nonlinear.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if the function is linear or nonlinear, we can examine the relationship between the x-values and corresponding y-values.

For a function to be linear, the change in y should be proportional to the change in x. In other words, the slope of the function should remain constant.

Calculating the change in y and x-values:

For the first set of points:

y = 3
x = 0

For the second set of points:

y = 6
x = 6

Change in y = 6 - 3 = 3
Change in x = 6 - 0 = 6

For the third set of points:

y = 12
x = 18

Change in y = 12 - 6 = 6
Change in x = 18 - 6 = 12

Comparing the change in y to the change in x for each set of points:

For the first set of points: Change in y / Change in x = 3 / 6 = 0.5
For the second set of points: Change in y / Change in x = 3 / 6 = 0.5
For the third set of points: Change in y / Change in x = 6 / 12 = 0.5

Since the ratio of the change in y to the change in x is the same for all sets of points, the function is linear.