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Conditions for a Relation to Be a Function

publish date: 2026/05/23 18:47:49.346654 UTC

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A relation \(f: A \to B\) is called a function when two conditions hold. Which of the following are those two conditions? (Select both.)

Each element of A is involved in the relation (no element of A is left without an image)

Each element of A is associated to exactly one element of B (not more than one)

Each element of B is involved in the relation

No element of B has more than one pre-image

The domain and codomain must be equal sets

(1) Each element of A is involved in the relation (no element of A is left without an image)

(2) Each element of A is associated to exactly one element of B (not more than one)

The two conditions are both restrictions on elements of the domain A (not on B):

No restriction is placed on elements of the codomain \(B\) — that is what distinguishes a general function from injective or surjective functions.

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012