Domain and Range From a Relation

1) Identify the ordered pairs

A relation is often given as a set of ordered pairs, a table, or another listing of inputs and outputs. For domain and range, focus on the pairs themselves.

• The domain is the set of all first coordinates, or input values.
• The range is the set of all second coordinates, or output values.

2) List the domain

Go through each ordered pair and collect the first number from each one.

• Write each input only once.
• If a value appears more than once, keep it just one time.
• Put the final set in simplified form, usually in braces.

3) List the range

Now collect the second number from each ordered pair.

• Again, repeat values are written only once.
• Make sure no output is left out.
• Simplify the final set.

4) Check your answer

A good check is to compare your lists with the original relation:

• Every input should appear in the domain.
• Every output should appear in the range.
• No extra values should be added.

If the relation is written in a different format, first rewrite it as ordered pairs if possible. Then separate the first and second coordinates carefully. The main goal is accuracy and removing duplicates.