Which relation is displayed in this table?

Responses

{(2, 1), (4,  3), (6, 5), (8,7)}
left bracket begin ordered pair 2 comma 1 end ordered pair comma begin ordered pair 4 comma 3 end ordered pair comma begin ordered pair 6 comma 5 end ordered pair comma begin ordered pair 8 comma 7 end ordered pair right bracket

{(1,  2), (3,  4), (5, 6), (7, 8)}
left bracket begin ordered pair 1 comma 2 end ordered pair comma begin ordered pair 3 comma 4 end ordered pair comma begin ordered pair 5 comma 6 end ordered pair comma begin ordered pair 7 comma 8 end ordered pair right bracket

{(1,  2), (3,  4), (5, 6), (8, 7)}
left bracket begin ordered pair 1 comma 2 end ordered pair comma begin ordered pair 3 comma 4 end ordered pair comma begin ordered pair 5 comma 6 end ordered pair comma begin ordered pair 8 comma 7 end ordered pair right bracket

{(2, 1), (4,  3), (6, 5), (7,8)}
left bracket begin ordered pair 2 comma 1 end ordered pair comma begin ordered pair 4 comma 3 end ordered pair comma begin ordered pair 6 comma 5 end ordered pair comma begin ordered pair 7 comma 8 end ordered pair right bracket
x y
1 2
8 7
5 6
3 4

1 answer

The given table displays a relation between two sets of numbers (x-values and y-values) through ordered pairs. Let's analyze the relation:

Based on the ordered pairs provided:

  1. The first set of ordered pairs: {(2, 1), (4, 3), (6, 5), (8, 7)}
  2. The second set of ordered pairs: {(1,  2), (3,  4), (5, 6), (7, 8)}
  3. The third set of ordered pairs: {(1,  2), (3,  4), (5, 6), (8, 7)}
  4. The fourth set of ordered pairs: {(2, 1), (4,  3), (6, 5), (7,8)}

The last section shows the alignment of x-values and y-values:

  • (1, 2)
  • (8, 7)
  • (5, 6)
  • (3, 4)

To summarize:

  • In the first example, for every even x-value (2, 4, 6, 8), there is a corresponding y-value by subtracting 1 from the x-value (x-1 or y=x-1).
  • In the second example, the x-values are all odd and correspond to consecutive even numbers beginning from 2.
  • The third example is similar to the second but includes pairs based on different numbers.
  • The fourth has one ordered pair that changes slightly but ultimately speaks to a similar reduction logic.

To determine which relation is being represented, we can conclude that the patterns depict a linear relationship based on a simple arithmetic operation between the x and y coordinates.

The overall consistent transformation present in the provided tables implies these relations likely follow a consistent numeric pattern or a simple function-like mapping.