Determine whether each relation defines a function. See Example 1.

Key Concepts

Relation

A relation is a set of ordered pairs, where each pair consists of an input (or domain element) and an output (or range element). In the context of functions, a relation can be represented as a graph, a table, or a set of points. Understanding relations is crucial for determining whether a specific relation meets the criteria to be classified as a function.

Function

A function is a specific type of relation where each input is associated with exactly one output. This means that for every x-value in the domain, there is only one corresponding y-value in the range. To determine if a relation is a function, one can use the vertical line test on its graph: if a vertical line intersects the graph at more than one point, the relation is not a function.

Vertical Line Test

The vertical line test is a visual method used to determine if a relation is a function by examining its graph. If any vertical line drawn through the graph intersects it at more than one point, the relation fails the test and is not a function. This test provides a straightforward way to assess the uniqueness of outputs for each input in a relation.