Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Key Concepts

Function Definition

A function is a specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that for every x-value in the domain, there must be one and only one corresponding y-value. Understanding this definition is crucial for determining whether a given relation qualifies as a function.

Domain and Range

The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Identifying the domain and range helps in understanding the behavior of the function and its limitations. It is essential to analyze the relation to accurately determine these sets.

Vertical Line Test

The vertical line test is a visual method used to determine if a relation is a function. If a vertical line drawn through the graph of the relation intersects it at more than one point, the relation is not a function. This test provides a quick way to assess the function property of a relation graphically.