Help creating a function diagram

May 2010
6
0
Virginia
My name is Katie.
I'm working with a book called Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley. This chapter is entitled Functions and Relations and this section is focusing on iterated function sequences.

They want me to give a complete diagram for the function f below:

function f : {1, 2, 3, ... 32} --> {1, 2, 3, ... 32} given by

f(x) = 11 + [x/3]

(In the book, the "[]" brackets are actually half brackets that look like upside down L's)

I don't even know what kind of diagram they mean or how to do it. If anyone could help me, that would be great. Thank you in advance.
 

Plato

MHF Helper
Aug 2006
22,461
8,632
They want me to give a complete diagram for the function f below:
function f : {1, 2, 3, ... 32} --> {1, 2, 3, ... 32} given by
f(x) = 11 + [x/3]
The function \(\displaystyle f(x) = 11 + \left\lceil {\frac{x}{3}} \right\rceil \) involves the ceiling function(the least integer greater or equal to the number).
For some examples: \(\displaystyle f(1)=12,~f(15)=16~\&~f(32)=22\).
I would guess that the text simply wants you to draw the graph.
 
May 2010
6
0
Virginia
The function \(\displaystyle f(x) = 11 + \left\lceil {\frac{x}{3}} \right\rceil \) involves the ceiling function(the least integer greater or equal to the number).
For some examples: \(\displaystyle f(1)=12,~f(15)=16~\&~f(32)=22\).
I would guess that the text simply wants you to draw the graph.
Thank you for your post! Okay I think I understand that. But how do you get f(1)=12? I think I'll be able to draw the graph once I understand how you get the series.
 

Plato

MHF Helper
Aug 2006
22,461
8,632
Here are more examples.
\(\displaystyle \left\lceil {\frac{1}
{3}} \right\rceil = 1,~\left\lceil {\frac{3}
{3}} \right\rceil = 1,~\left\lceil {\frac{4}
{3}} \right\rceil = 2,~\left\lceil {\frac{6}
{3}} \right\rceil = 2,~\left\lceil {\frac{8}
{3}} \right\rceil = 3\)
The next integer.
 
May 2010
6
0
Virginia
Here are more examples.
\(\displaystyle \left\lceil {\frac{1}
{3}} \right\rceil = 1,~\left\lceil {\frac{3}
{3}} \right\rceil = 1,~\left\lceil {\frac{4}
{3}} \right\rceil = 2,~\left\lceil {\frac{6}
{3}} \right\rceil = 2,~\left\lceil {\frac{8}
{3}} \right\rceil = 3\)
The next integer.
Ohh! Now it makes sense! Thank you so much! (Rock)