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

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 input values from the given relation: 9, -3, and 9.
3. Check if any input value is repeated with different outputs. Here, the input 9 appears twice with outputs -2 and 1.
4. Since the input 9 corresponds to two different outputs (-2 and 1), this violates the definition of a function.
5. Conclude that the given relation does not define a function because one input has multiple outputs.

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.

Relation as a Set of Ordered Pairs

A relation is a collection of ordered pairs, where the first element is the input and the second is the output. Understanding how to interpret these pairs is essential to analyze whether the relation meets the criteria of a function.

Testing for Function Using Ordered Pairs

To determine if a relation is a function, check if any input value repeats with different outputs. If an input appears more than once with different outputs, the relation is not a function.