Question

Which of the following relations are not functions? Select all that apply.  {(1, 3), (3, 7), (5, 11), (7, 15), (9, 19)}  {(1, 3), (1, 7), (5, 11), (5, 15), (9, 19)}  {(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4)}  {(2, 4), (1, 1), (0, 0), (1,−1), (2, −4)}  {(6, 3), (4, 1), (2, 1), (0,−1), (−2,−3)}  {(1, 3), (3, 7), (3, 11), (7, 15), (9, 19)}  {(1, 3), (3, 7), (5, 11), (9, 15), (9, 19)}

Answer 1

Given:

7 relations are given.

To find:

The relation which is not a function.

Step-by-step explanation:

A relation is called function if there exist unique output for each input.

It means, each x-value has only one y-value.

{(1, 3), (3, 7), (5, 11), (7, 15), (9, 19)}, it is a function.

{(1, 3), (1, 7), (5, 11), (5, 15), (9, 19)}, it is not a function because there exist two y-values y=3 and y=7 at x=1.

{(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4)}, it is a function.

{(2, 4), (1, 1), (0, 0), (1,−1), (2, −4)},it is not a function because there exist two y-values y=4 and y=-4 at x=2.

{(6, 3), (4, 1), (2, 1), (0,−1), (−2,−3)}, it is a function.

{(1, 3), (3, 7), (3, 11), (7, 15), (9, 19)}, it is not a function because there exist two y-values y=7 and y=11 at x=3.

{(1, 3), (3, 7), (5, 11), (9, 15), (9, 19)}, it is not a function because there exist two y-values y=15 and y=19 at x=9.

Therefore, the correct options are 2, 4, 6 and 7.