Determine whether each relation defines a function. See Example 1. {(8,0),(5,7),(9,3),(3,8)}

Verified step by step guidance

1. Identify the definition of a function: A relation is a function if each input (or x-value) is associated with exactly one output (or y-value).
2. List the x-values from the given relation: 8, 5, 9, 3.
3. Check if any x-value is repeated in the list: 8, 5, 9, 3 are all unique.
4. Since no x-value is repeated, each input has exactly one output.
5. Conclude that the relation is a function because each x-value is paired with only one y-value.

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 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 given, each pair is of the form (x, y). Analyzing these pairs helps in checking if any x value repeats with a different y value, which would indicate that the relation is not 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. This concept is useful for visual learners and can be applied to the set of ordered pairs by plotting them on a coordinate plane.