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Identify the Function Type From a Diagram

publish date: 2026/05/23 18:47:50.705117 UTC

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Look at the mapping below — four domain elements map to three codomain elements.

What type of function is shown?

One-one (injective) — distinct inputs give distinct outputs

Bijective — one-one and onto

Many-one and onto — not injective, but surjective

Not a function — an element has two images

Correct Answer

Many-one and onto — not injective, but surjective

Explanation

In the diagram, \(b\) and \(d\) both map to \(2\) — so the function is many-one (not injective). However, every element of the codomain (\(1, 2, 3\)) is an image: \(1 \leftarrow a\), \(2 \leftarrow b, d\), \(3 \leftarrow c\) — so it is onto (surjective). A function can be surjective without being injective, and vice versa.

Reference

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

Quizzes you can take where this question appears

Types of Functions