Check all the ways we could represent a relation:

Question

Answer,
An x-y or input-output table

Answer,
A set of ordered pairs

Answer,
A mapping diagram

Answer,
A Venn diagram

Answer,
A frequency table

Answer,
A histogram

Answer 1

To represent a relation, the appropriate methods are:

1. An x-y or input-output table - This is a valid representation, as it lists pairs of inputs (x) and their corresponding outputs (y).

2. A set of ordered pairs - This is also a valid representation, as relations can be defined as sets of ordered pairs (e.g., {(1, 2), (3, 4)}).

3. A mapping diagram - This is a valid representation that visually depicts how each input is connected to its corresponding output.

The following methods are not typically used to represent a relation:

4. A Venn diagram - Not generally used for relations in the mathematical sense. Venn diagrams are better used for representing sets and their relationships.

5. A frequency table - This is used for summarizing data and showing how often each value occurs, not for representing relations.

6. A histogram - This graphical representation is used for displaying the distribution of numerical data, not typically for defining a relation.

In summary, the valid representations of a relation are:

• An x-y or input-output table
• A set of ordered pairs
• A mapping diagram