I have read several times that there exist many continuous functions whose Fourier series diverge at some points (sometimes even on a dense subset of the domain!). I tried to find an explicit example of them and the closest thing I found is This example by Fejer, a link from MSE. According to a comment responding to the question, it seems that Fejer's example cannot be represented by a graph. Here are my questions:
1.)What is the reason that the function cannot be represented by graph?
2.)Is there any function with the properties I mentioned that can be represented by graph?
3.)What is the intuitive reason that those functions have divergent Fourier series at some points?
I am aware that this question is a duplication of some already existing topics on MSE but none of the links I read give me a satisfactory answer. Also, could anyone give me a rough description of Fejer's function's behavior that explains why it can't be graphed? Thank you in advance.