Could you point me out some clear and extensive sources in this regard, please? I haven't found an interesting and extensive document so far.
I have knowledge about parent graphs of functions and their transformations but limited to simple opertations: like stretching/shrinking by multiplication with a costant greater/smaller than 1 and 0, reflection by multiplication by -1, vertical translations by sum and difference with constants and horizontal translations by sum and difference with constants inside products. However, I would like to have more clear in my mind the effects of more complex transformations due to operations between functions (like addition, subraction, multiplication, division, composition between 2 or more functions).
It is for getting more knowledge as I like it but also because I think it helps in order to study the function when there is to determine the right operation for finding its range - or am I wrong and it is useless the knowledge for which I am asking advice in order to find ranges of functions?
PS. You can make some examples of elementary functions and how to graph them, to render more concrete this question. Thus, I can also gain some knowledge from your examples.