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We define the quantities:

$\lfloor x\rfloor$=$supremum \{n∈{\Bbb Z}:n≤x\}$

and

$\lceil x\rceil=minimum\{n∈{\Bbb Z}:n≥x\}$

Sketch the graph of the functions defined by the mapping rules:

$(a)f_1=\lfloor x\rfloor$

$(b)f_2=\lceil x\rceil$

$(c)f_3=\lceil x\rceil-\lfloor x\rfloor$

$(d)f_4=x-\lfloor x\rfloor$$

$(e)f_5=\frac{x}{\lvert x\rvert}$

I just want to know how to graph $\lfloor x\rfloor$ or $\lceil x\rceil$ because I can not find or I do not see any way to how to do it

any hint will be well received

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    $\begingroup$ Just plug in some values for $x$ and see how the function behaves. Also, there is a lot of infomation about such functions on the Internet (since you used those latex commands I guess you know how they're called). $\endgroup$ – CIJ Sep 23 '15 at 23:03
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    $\begingroup$ I did not know, but now I know that they are called Floor and Ceiling functions, and as you say, there is a lot of information on the internet, thanks mate. :) $\endgroup$ – Iván Galeana Aguilar Sep 23 '15 at 23:22
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hint: $$\lfloor x \rfloor= t, \text{if $t \leq x < t+1$ and $t \in \mathbb{Z}$} \\ \lceil x \rceil= t,\text{if $t-1 < x \leq t$ and $t \in \mathbb{Z}$}$$

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Here is a graph of your functions:

enter image description here

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