Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

Verified step by step guidance

1. Understand the definition of a function: A relation is a function if every input (or domain value) corresponds to exactly one output (or range value). This means no input is paired with more than one output.
2. Identify the domain: List all the input values from the given relation. The domain is the set of all these input values.
3. Identify the range: List all the output values from the given relation. The range is the set of all these output values.
4. Check if the relation is a function by verifying that each input in the domain maps to only one output in the range. If any input corresponds to multiple outputs, the relation is not a function.
5. Summarize your findings by stating whether the relation is a function, and clearly write down the domain and range sets using set notation, for example, \(\{x_1, x_2, \ldots\}\) for domain and \(\{y_1, y_2, \ldots\}\) for range.

Key Concepts

Definition of a Function

A function is a relation where each input (domain element) corresponds to exactly one output (range element). This means no input value can be paired with more than one output value. Understanding this helps determine if a given relation qualifies as a function.

Domain of a Relation

The domain is the set of all possible input values for the relation. Identifying the domain involves listing or describing all the first elements in the ordered pairs or inputs for which the relation is defined.

Range of a Relation

The range is the set of all possible output values that the relation can produce. It consists of all second elements in the ordered pairs or outputs corresponding to the domain values.