Determine whether each relation defines a function, and give the domain and range.

Verified step by step guidance

1. Step 1: Identify the points in the relation from the graph. Here, the graph shows a single point at (-2, -4) with two arrows pointing to it from the left, indicating multiple x-values mapping to the same y-value.
2. Step 2: Determine if the relation is a function by checking if each x-value corresponds to exactly one y-value. Since the graph shows only one point at x = -2, and no other x-values are shown, each x-value maps to one y-value, so this relation can be considered a function.
3. Step 3: Find the domain, which is the set of all x-values in the relation. From the graph, the only x-value is -2, so the domain is { -2 }.
4. Step 4: Find the range, which is the set of all y-values in the relation. From the graph, the only y-value is -4, so the range is { -4 }.
5. Step 5: Summarize: The relation defines a function because each x-value has exactly one y-value. The domain is { -2 } and the range is { -4 }.

Key Concepts

Definition of a Function

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

Domain of a Relation

The domain is the set of all possible input values (x-values) in a relation. Identifying the domain involves listing all x-values that appear in the relation, which is essential for understanding the scope of the function or relation.

Range of a Relation

The range is the set of all possible output values (y-values) in a relation. Determining the range involves listing all y-values that the relation maps to, which helps describe the behavior and output limits of the function or relation.