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Draw graphs of each of these functions.

  1. $f(x) =$ $\left \lceil 3x-2 \right \rceil$
  2. $f(x) =$ $\left \lceil 0.2x \right \rceil$
  3. $f(x) =$ $\left \lfloor -1/x \right \rfloor$
  4. $f(x) =$ $\left \lfloor x^2 \right \rfloor$
  5. $f(x) =$ $\left \lceil x/2 \right \rceil\left \lfloor x/2 \right \rfloor$
  6. $f(x) =$ $\left \lfloor x/2 \right \rfloor + \left \lceil x/2 \right \rceil$
  7. $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$

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Pooja Khatri asked Apr 11, 2019
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Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $|A|=|B|$. Show that $f$ is one-to-one if and only if it is onto.