Domain of Variable/Examples
Examples of Domains of Variables
Litres of Water in Washing Machine
Let $V$ be the number of litres of water in a washing machine.
The domain of $V$ is the closed interval $\closedint 0 C$, where $C$ is the capacity of the washing machine.
$V$ is a continuous variable.
Books on Library Shelf
Let $B$ be the number of books on a library shelf.
The domain of $B$ is the closed interval $\closedint 0 C$, where $C$ is the largest number of books that can be held on a shelf.
$B$ is a discrete variable.
Points on Pair of Dice
Let $S$ be the total number of points that are obtained when tossing a pair of dice.
The domain of $S$ is the set $\set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}$.
$S$ is a discrete variable.
Diameter of Sphere
Let $d$ be the diameter of a sphere.
The domain of $d$ is the open interval $\openint 0 \to$.
$d$ is a continuous variable.
Countries in Europe
Let $C$ be a country in Europe.
The domain of $C$ is the set $\set {\text {France}, \text {Germany}, \text {Spain}, \text {Italy}, \ldots}$
These can be represented numerically if desired, by assigning an integer to each of the countries in Europe, for example:
- $1: \text {France}$
- $2: \text {Germany}$
- $3: \text {Spain}$
- $4: \text {Italy}$
- $\vdots$
$C$ is a discrete variable.
Arbitrary Example
Let $f$ be the function:
- $\map f x = \dfrac 1 {\sqrt {4 - x^2} }$
The domain of $f$ is the open interval $\openint {-2} 2$, that is, where $-2 < x < 2$.