a.

nonlinear

b.

linear

c.

linear and nonlinear

d.

neither linear nor nonlinear

D

Step-by-step explanation:

Given the table

The change in x is

The change in y is

Since for the same change in x, the change in y is different, given table represents nonlinear function.

C

Step-by-step explanation:

The table shows linear function.

Check it.

1. From x = 1 to x = 2 (change in x is +1), y changes from 6 to 8 (that is +2)

2. From x = 2 to x = 3 (change in x is +1), y changes from 8 to 10 (that is +2)

3. From x = 3 to x = 4 (change in x is +1), y changes from 10 to 12 (that is +2)

4. From x = 4 to x = 5 (change in x is +1), y changes from 12 to 14 (that is +2)

This means for constant change in x (+1) there is a constant change in y (+2), so the function represented by given table is linear.

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