Question

1. A relation contains the ordered pairs shown. One of the ordered pairs is missing an x-coordinate. {(-1,4),(0,4),(2,5),(3,-6),(?,7)} What could be the missing x-coordinate if the relation is not a function?

Answer 1

There are 4 possible scenarios where given relation could not be a function:

i)
`(-1, 4), (0,4), (2,5), (3,-6), (-1, 7)`

ii)
`(-1, 4), (0,4), (2,5), (3,-6), (0, 7)`

iii)
`(-1, 4), (0,4), (2,5), (3,-6), (2, 7)`

iv)
`(-1, 4), (0,4), (2,5), (3,-6), (3, 7)`

Explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)
`(-1, 4), (0,4), (2,5), (3,-6), (-1, 7)`

ii)
`(-1, 4), (0,4), (2,5), (3,-6), (0, 7)`

iii)
`(-1, 4), (0,4), (2,5), (3,-6), (2, 7)`

iv)
`(-1, 4), (0,4), (2,5), (3,-6), (3, 7)`