Domain in Context
Aligned to F-IF.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
The domain is the set of allowable inputs. In real situations the domain is often limited to values that make sense — you cannot have negative time or a fraction of a person.
Worked examples
Example 1
A ticket function T(n) = 12n gives the cost for n tickets. Since you can only buy whole numbers of tickets that are 0 or more, the domain is the whole numbers 0, 1, 2, 3, ….
Example 2
A rectangle of perimeter 20 has area A(w) = w(10 − w). The domain is 0 < w < 10, because a side cannot be zero or negative.
Example 3
The algebra rarely knows the context. x² is defined for every real number; the number of tickets sold is not.
Practice questions
- A pool drains over time t. Why must the domain have t ≥ 0?
- A function gives the cost for n students on a trip. State a reasonable domain.
- Why can't the number of cars counted in a lot be 3.5?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
El Dominio en Contexto
El dominio es el conjunto de entradas permitidas. En situaciones reales el dominio suele limitarse a valores con sentido: no puede haber tiempo negativo ni una fracción de persona.
Ejemplo 1: Una función de boletos T(n) = 12n da el costo para n boletos. Como solo puedes comprar cantidades enteras de boletos de 0 o más, el dominio son los enteros 0, 1, 2, 3, ….
Ejemplo 2: Un rectángulo de perímetro 20 tiene área A(a) = a(10 − a). El dominio es 0 < a < 10, porque un lado no puede ser cero ni negativo.
Ejemplo 3: El álgebra casi nunca conoce el contexto. x² está definida para todo real; el número de boletos vendidos no.
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