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  1. \(f\) is injective, but not surjective (since 0, for example, is never an output).

  2. \(f\) is injective and surjective. Unlike in the previous question, every integers is an output (of the integer 4 less than it).

  3. \(f\) is injective, but not surjective (10 is not 8 less than a multiple of 5, for example).

  4. \(f\) is not injective, but is surjective. Every integer is an output (of twice itself, for example) but some integers are outputs of more than one input: \(f(5) = 3 = f(6)\text{.}\)

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