In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(1, 4), (1, 5), (1, 6)}

Verified step by step guidance

1. Recall that a relation is a function if each input (or x-value) corresponds to exactly one output (or y-value).
2. Examine the given relation: \(\{(1, 4), (1, 5), (1, 6)\}\). Notice that the input value 1 is paired with multiple outputs (4, 5, and 6).
3. Since the input 1 corresponds to more than one output, this relation is not a function.
4. Identify the domain by listing all unique input values. Here, the domain is \(\{1\}\) because 1 is the only input.
5. Identify the range by listing all output values. Here, the range is \(\{4, 5, 6\}\) because these are all the outputs paired with the input.

Key Concepts

Definition of a Function

A function is a relation where each input (domain element) corresponds to exactly one output (range element). If any input is paired with more than one output, the relation is not a function. This concept helps determine if the given set of ordered pairs qualifies as a function.

Domain of a Relation

The domain is the set of all first elements (inputs) in the ordered pairs of a relation. Identifying the domain involves listing all unique x-values from the given pairs, which is essential for understanding the inputs the relation covers.

Range of a Relation

The range is the set of all second elements (outputs) in the ordered pairs of a relation. Finding the range involves listing all unique y-values from the pairs, which shows all possible outputs the relation produces.