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 x-value) corresponds to exactly one output (or y-value). This means no x-value is paired with more than one y-value.
2. Examine the given relation by listing all the input-output pairs. Check if any input (x-value) appears more than once with different outputs (y-values). If it does, the relation is not a function.
3. Identify the domain of the relation by collecting all the unique input values (x-values) from the pairs. The domain is the set of all these x-values.
4. Identify the range of the relation by collecting all the unique output values (y-values) from the pairs. The range is the set of all these y-values.
5. Summarize your findings: state whether the relation is a function based on the previous check, and clearly list the domain and range sets.

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 is 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 all unique first elements from the ordered pairs or the allowable input values in the relation.

Range of a Relation

The range is the set of all possible output values that the relation maps to. It consists of all unique second elements from the ordered pairs or the resulting values from the function's rule.