What do mathematicians use to make graphs for analysis textbooks? Apologies if this is not the correct SE for this.
I have been transferring all of my notes to LaTeX and I have been wanting to include some custom diagrams. I often find my self having to find images to add to my notes but they are not quite what I want. I have tried using different graphic software but nothing seems to do it properly. Could anybody suggest to me any software through which I could make diagrams like this?:

 A: One alternative I have used many times is mathcha.io. It lets you create visually and it outputs Tikz ready to include in your document.
A: I would suggest Tikz libraries for Latex, which allows you to draw pretty much anything. It is time consuming to learn (and to draw), but results are fantastic. For instance, you guarantee that the letter type in a figure coincides with that in the body of your notes, something which is not in general true when you use other software. The manual is here http://pgf.sourceforge.net/pgf_CVS.pdf
A: I use Mathematica exclusively, and have published perhaps 1000 figures created with it.  Here's just a start on yours:

Yes, use MaTeX to add LaTeX expressions in such figures:

Here's a more detailed explanation.
A: Ipe
Ipe is a free drawing editor, easy enough to learn, can produce output with LaTeX/Tikz/PDF/etc., and is pretty powerful. It takes only a minute or two to recreate your diagram. (The arrow heads can even be fine tunes to match those you used, but I'll leave that to you):

