Algebra 1 · Unit 4 · Topic 4.3
Domain, Range, and Context Restrictions
The domain is the set of allowed inputs; the range is the set of outputs actually produced.
Definition and explanation
The domain is the set of allowed inputs; the range is the set of outputs actually produced. Algebraic restrictions and real-world restrictions both matter, such as excluding division by zero or negative counts of objects.
Worked example
For C(n) = 5 + 2n, where n is the number of purchased notebooks and 0 ≤ n ≤ 3, the domain is {0, 1, 2, 3}. The range is {5, 7, 9, 11} dollars, not every number between 5 and 11.
Common mistake
A formula alone does not require a continuous domain when the context uses whole-number counts.
Key takeaway
The domain is the set of allowed inputs; the range is the set of outputs actually produced.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.