Determine whether each relation defines a function. {(5,1),(3,2),(4,9),(7,8)}

Verified step by step guidance

1. Recall that a relation defines a function if every input (or x-value) corresponds to exactly one output (or y-value). In other words, no x-value should repeat with a different y-value.
2. List the x-values from the given relation: 5, 3, 4, and 7.
3. Check if any x-value appears more than once with different y-values. Here, each x-value (5, 3, 4, 7) appears only once.
4. Since no x-value is repeated with a different 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 these pairs helps identify patterns or violations of function rules. Recognizing how to interpret and examine these pairs is key to solving the problem.

Testing for Function Using Domain Values

To check if a relation is a function, examine the domain values (first elements) in each ordered pair. If any domain value repeats with different range values, the relation is not a function. This method provides a straightforward way to verify the function property.