# Can anyone give me a hint of how to graph the following functions?

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$$(e)f_5=\frac{x}{\lvert x\rvert} I just want to know how to graph \lfloor x\rfloor or \lceil x\rceil because I can not find or I do not see any way to how to do it any hint will be well received • Just plug in some values for x and see how the function behaves. Also, there is a lot of infomation about such functions on the Internet (since you used those latex commands I guess you know how they're called). – CIJ Sep 23 '15 at 23:03 • I did not know, but now I know that they are called Floor and Ceiling functions, and as you say, there is a lot of information on the internet, thanks mate. :) – Iván Galeana Aguilar Sep 23 '15 at 23:22 ## 2 Answers hint:$$\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$t \in \mathbb{Z}$}$\$

Here is a graph of your functions: