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

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Recall that a relation defines a function if every input (x-value) corresponds to exactly one output (y-value).

List the input values from the given relation: -3, 4, and -2.

Check if any input value is repeated with a different output value. Here, -3, 4, and -2 each appear only once.

Since no input value is paired with more than one output value, the relation satisfies the definition of a function.

Conclude that the given relation defines a function because each input has a unique output.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 represents a relationship between elements of two sets, often shown as points or pairs.

Definition of a Function

A function is a special type of relation where each input corresponds to exactly one output. This means no x-value can be paired with more than one y-value in the set.

Testing a Relation for Function Status

To determine 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.

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Textbook Question

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

Textbook Question

Let $ƒ (x) = x^{2} + 3$ and $g (x) = - 2 x + 6$ . Find each of the following. See Example 1.