Onto (Surjective) Function — Identify From a Diagram

Onto (surjective): every codomain element has at least one pre-image

Explanation

A function \(f: A \to B\) is onto (surjective) if every element of the codomain is the image of at least one domain element. Here: \(1\) ← \(a\), \(2\) ← \(b\) and \(c\), \(3\) ← \(d\) — every codomain element is hit. Note that \(2\) has two pre-images (\(b\) and \(c\)), so the function is not injective — but surjectivity only requires each codomain element to be hit at least once.