Question

3. Is this relation a function? (-1,5) (-3, 6) (-2, 9) (5, 11) (-3, 6) (4, 11) (0, 10)​

Answer 1

Yes, it is.

Explanation:

A function is a relation between two sets of elements, where each valid input can be mapped to exactly one output.

Indeed, the relation in this question is between two sets of elements. Each of these pairs includes exactly two elements: the input and the output.

On the other hand, does this relation maps each valid input to exactly one output? Arrange these pairs by the input in increasing order:

• Input:
  `-3`; Output:
  `6`.
• Input:
  `-3`; Output:
  `6`.
• Input:
  `-2`; Output:
  `9`.
• Input:
  `-1`; Output:
  `5`.
• Input:
  `0`; Output:
  `10`.
• Input:
  `4`; Output:
  `11`.
• Input:
  `5`; Output:
  `11`.

Indeed, the input
`-3` appeared twice in the list. However, in both occurrence, this input mapped to the same output,
`6`. This relation is still a function.