Determine whether each relation defines a function. {(-12,5),(-10,3),(8,3)}

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: -12, -10, and 8.
3. Check if any input value is repeated with a different output value. Here, -12, -10, and 8 each appear only once.
4. Since no input value is repeated with different outputs, each input has exactly one output.
5. Conclude that the given relation does define a function because each input maps to a unique output.

Key Concepts

Definition of a Relation

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value). It shows how elements from one set correspond to elements in another set. Understanding relations is fundamental to analyzing whether they meet the criteria of a function.

Definition of a Function

A function is a special type of relation where each input (x-value) is paired with exactly one output (y-value). This means no x-value can appear more than once with different y-values. Recognizing this helps determine if a given relation qualifies as a function.

Testing a Relation for Functionality

To test if a relation is a function, check if any x-values repeat with different y-values. If all x-values are unique or repeated with the same y-value, the relation is a function. This method is essential for evaluating sets of ordered pairs like the one given.