Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4. x y 0 0 -1 1 -2 2

Verified step by step guidance

1. Step 1: Understand the definition of a function. A relation defines a function if every input (x-value) corresponds to exactly one output (y-value).
2. Step 2: Examine the given pairs: (0, 0), (-1, 1), and (-2, 2). Check if any x-value repeats with a different y-value. Here, all x-values are unique.
3. Step 3: Since each x-value has only one corresponding y-value, conclude that the relation does define a function.
4. Step 4: Determine the domain by listing all the x-values from the relation: \(\{0, -1, -2\}\).
5. Step 5: Determine the range by listing all the y-values from the relation: \(\{0, 1, 2\}\).

Key Concepts

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if a relation is a function, check that no x-value is paired with more than one y-value.

Domain of a Relation

The domain is the set of all possible input values (x-values) in the relation. Identifying the domain involves listing all unique x-values from the given pairs.

Range of a Relation

The range is the set of all possible output values (y-values) in the relation. To find the range, list all unique y-values corresponding to the inputs in the relation.