Diagram — Is This Function Onto?

No — element 3 in the codomain has no pre-image in A

Explanation

For surjectivity, every element of the codomain must be the image of at least one domain element. In this diagram, element \(3\) (shown greyed out) is never hit — neither \(a\), \(b\), nor \(c\) maps to it. Therefore the range is only \(\{1, 2\}\) which is a proper subset of the codomain \(\{1, 2, 3\}\), so the function is not onto.