M208 - TMA01 / Part 2

Started working on it today. The exercises aren't really difficult, I suppose. Well, everything can be turned into a challenge. I am trying to do as much as I can with Mathematica, that way I learn more about Mathematica. I am trying to find a way to visualize the effect of a linear translation on a certain are of the 2D-plane at the moment. I sort of feel the load of the 90 points at the moment. Have to ship all questions by the end of next week.

A research problem which interests me is the Collatz 3x+1 function, which is defined as follows:

$$\begin{equation*} f(n)= \begin{cases} 3n+1 & \text{if $n$ odd ,} \\ \frac{n}{2} &\text{if $n$ even.} \end{cases} \end{equation*}$$
Collatz conjectured that recursively applying this function to a number always ends in the loop {1,4,2,1}.
Take for example 9.
f(9) = 28 , f(28)=14 , f(14)=7,  f(7)=22 , f(22)=11 ,f(11)=34 , f(34)=17 , f(17)=52, f(52)=26, f(13)=40 ,f(40)=20, f(20)=10 , f(10)=5 , f(5)=16, f(16)=8, f(8)=4 , f(4)=2, f(2)=1, f(1)=4
et voila...

Try 27, if you dare.