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

Verified step by step guidance

1. Recall that a relation defines a function if every input (x-value) corresponds to exactly one output (y-value).
2. List the x-values from the given relation: 8, 5, 9, and 3.
3. Check if any x-value repeats with a different y-value. In this case, each x-value appears only once.
4. Since no x-value is paired with more than one y-value, the relation satisfies the definition of a function.
5. Conclude that the given relation defines a function because each input has a unique output.

Key Concepts

Definition of a Function

A function is a relation where each input (or domain element) is paired with exactly one output (or range element). This means no input value can correspond to more than one output value. Understanding this definition is essential to determine if a given set of ordered pairs represents a function.

Relation as a Set of Ordered Pairs

A relation is a collection of ordered pairs, where the first element is from the domain and the second from the range. Analyzing the relation involves examining these pairs to see how inputs and outputs correspond. This helps in checking if the relation meets the criteria of a function.

Checking for Repeated Inputs

To determine if a relation is a function, look for repeated first elements (inputs) in the ordered pairs. If any input appears more than once with different outputs, the relation is not a function. This step is crucial for verifying the function property in a given set.