Roster Notation

Definition

Roster notation is a way to explicitly list all the elements of a set. In the context of domain and range, it provides a clear and specific representation of the possible values that the function can take for its inputs (domain) and outputs (range).

Roster Notation for Domain and Range

• Domain: When using roster notation to represent the domain of a function, you list all the possible input values explicitly. This method is most suitable when the set of inputs is finite or countable. For example:

  • If a function is defined only for the values x = 1, x = 2, and x = 3, the domain in roster notation is:

{1, 2, 3}

• Range: Similarly, roster notation for the range involves listing all possible output values explicitly. This method is typically used when the output values are discrete and finite. For example:

  • If the range of a function includes only the values y = 2, y = 4, and y = 6, the range in roster notation is:

{2, 4, 6}

Examples

1. Finite Domain: 

2. Suppose a function is defined for the integers 0, 1, 2, and 3. The domain in roster notation is:

{0, 1, 2, 3}

2. Finite Range: 

3. If a function maps inputs to the outputs 5, 10, and 15, the range in roster notation is:

{5, 10, 15}

Summary

Roster notation provides a straightforward way to represent sets by explicitly listing their elements. While it's particularly useful for finite sets, it can become impractical for infinite sets or ranges with continuous intervals, where other notations (like interval notation or set-builder notation) are more suitable.