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The following functions all have domain \(\{1,2,3,4,5\}\) and codomain \(\{1,2,3\}\text{.}\) For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective.

1. \(f = \twoline{1 \amp 2 \amp 3 \amp 4 \amp 5}{1 \amp 2 \amp 1 \amp 2 \amp 1}\text{.}\)

   • Injective

   • Surjective

   • Bijective

   • Neither

2. \(f = \twoline{1 \amp 2 \amp 3 \amp 4 \amp 5}{1 \amp 2 \amp 3 \amp 1 \amp 2}\text{.}\)

   • Injective

   • Surjective

   • Bijective

   • Neither

3. \(f(x) = \begin{cases} x \amp \text{ if } x \le 3 \\ x-3 \amp \text{ if } x \gt 3\end{cases}\text{.}\)

   • Injective

   • Surjective

   • Bijective

   • Neither