Domain and Range

Learn and apply domain and range using equations, examples, and interpretation.

Lesson 2 of 53 parts Practice Flashcards

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Domain

Objective: Explain and use domain in an Algebra 1 problem.

The domain is the set of permitted inputs, which may be restricted by algebra or by the context of a model. Division by zero is undefined.

Worked examples

Try itExample 1.1: For f(x)=1/(x−5), which input is excluded?Show answer

5. A denominator cannot equal zero. The answer is 5.

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Domain

Objective: Explain and use domain in an Algebra 1 problem.

The domain is the set of permitted inputs, which may be restricted by algebra or by the context of a model. Division by zero is undefined.

Worked examples

Try itExample 1.1: For f(x)=1/(x−5), which input is excluded?Show answer

5. A denominator cannot equal zero. The answer is 5.

Range

Objective: Explain and use range in an Algebra 1 problem.

The range is the set of actual outputs produced by the permitted inputs; it depends on the chosen domain. All nonnegative real numbers.

Worked examples

Try itExample 2.1: For f(x)=x²+25, what is the least output over real inputs?Show answer

25. The square cannot be negative, so adding 25 gives the minimum. The answer is 25.

Contextual Restrictions

Objective: Explain and use contextual restrictions in an Algebra 1 problem.

For a ticket model, an algebraic expression may accept real x but the context can require nonnegative integer counts. Elapsed time is nonnegative in that model.

Worked examples

Try itExample 3.1: For f(x)=1/(x−11), which input is excluded?Show answer

11. A denominator cannot equal zero. The answer is 11.

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