Determine whether each relation defines a function. See Example 1. {(-3,1),(4,1),(-2,7)}

Key Concepts

Definition of a Function

A function is a specific type of relation where each input (or 'x' value) is associated with exactly one output (or 'y' value). This means that for any given x, there cannot be two different y values. Understanding this definition is crucial for determining whether a given relation qualifies as a function.

Ordered Pairs

Relations are often represented as sets of ordered pairs, where each pair consists of an input and its corresponding output. In the example provided, the pairs are {(-3,1), (4,1), (-2,7)}. Analyzing these pairs helps in identifying if any input is repeated with different outputs, which would disqualify the relation from being a function.

Vertical Line Test

The vertical line test is a visual method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the relation is not a function. While this test applies to graphical representations, it reinforces the concept that each input must map to a single output.