Question

Which of the following relations has a domain of {-2, 0, 5}? Choose all that apply. {(-2, 5), (3, 4), (5, 1)} {(-2, 3), (0, 1), (-2, 4), (5, 4)} {(5, 6), (0, 4), (-2, 1)} {(4, -2), (3, 0), (2, 5)}

Answer 1

Second option: {
`(-2, 3), (0, 1), (-2, 4), (5, 4)`}

Third option: {
`(5, 6), (0, 4), (-2, 1)`}

Explanation:

By definition, the Domain of a relation is the set of all the x-coordinates of the ordered pairs (It is necessary to remember that the x-coordinate is the first element of the ordered pair).

Then, we know that the set of all the x-coordinates of the relation we need to find is: {
`-2, 0, 5`}

First option {
`(-2, 5), (3, 4), (5, 1)`}:

Domain: {
`-2, 3, 5`}

Second option {
`(-2, 3), (0, 1), (-2, 4), (5, 4)`}:

Domain: {
`-2, 0, 5`} (Notice that we do not need to write -2 twice)

Third option {
`(5, 6), (0, 4), (-2, 1)`}:

Domain: {
`-2, 0, 5`}

Fourth option {
`(4, -2), (3, 0), (2, 5)`}:

Domain: {
`2, 3, 4`}

The relations {
`(-2, 3), (0, 1), (-2, 4), (5, 4)`} and {
`(5, 6), (0, 4), (-2, 1)`} has a Domain of {
`-2, 0, 5`}