In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(-3, -3), (-2, −2), (−1, −1), (0, 0)}

Verified step by step guidance

1. Recall that a relation is a function if every input (x-value) corresponds to exactly one output (y-value).
2. Examine the given set of ordered pairs: \(\{(-3, -3), (-2, -2), (-1, -1), (0, 0)\}\). Check if any x-values repeat with different y-values.
3. Since all x-values (-3, -2, -1, 0) are unique and each maps to exactly one y-value, this relation is a function.
4. To find the domain, list all the x-values from the ordered pairs: \(\{-3, -2, -1, 0\}\).
5. To find the range, list all the y-values from the ordered pairs: \(\{-3, -2, -1, 0\}\).

Key Concepts

Definition of a Function

A function is a relation where each input (or domain element) corresponds to exactly one output (or range element). This means no two ordered pairs can have the same first element with different second elements. Understanding this helps determine if a given set of ordered pairs is a function.

Domain of a Relation

The domain is the set of all possible input values (first elements) in a relation. Identifying the domain involves listing all unique x-values from the ordered pairs. This is essential for understanding the scope of the relation.

Range of a Relation

The range is the set of all possible output values (second elements) in a relation. To find the range, list all unique y-values from the ordered pairs. Knowing the range helps describe the outputs the relation can produce.