Only to clarify my thoughts in question 5.

k (break point) is a fix value for a given type of hypothesis (problem) .

k do not depend of N, it is bound to N. Correct?

Also there is 2 option for growth function:

1-if there is not a break point then

2-if there is break point

, which is polynomial of degree k

So a grow function which it is polynomial with degree variable and depending of N could not be limited by

because for big value of N the bound will not be valid.

Am I right?