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Which functions are surjective (i.e., onto)?

  1. \(f:\Z \to \Z\) defined by \(f(n) = 3n\text{.}\)

  2. \(g: \{1,2,3\} \to \{a,b,c\}\) defined by \(g = \begin{pmatrix}1 \amp 2 \amp 3 \\ c \amp a \amp a \end{pmatrix}\text{.}\)

  3. \(h:\{1,2,3\} \to \{1,2,3\}\) defined as follows:

    Two rows containing the numbers 1, 2, and 3, from left to right.  Arrows from the top 1 to bottom 2, from the top 2 to bottom 1, and top 3 straight down to bottom 3.
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