The discussion centers on the periodicity of the function tan|x|, exploring whether it is periodic and the rules for determining the periodicity of functions in general. Participants also reference other functions such as ln(sin(x)) and e^sin(x) in this context.
Participants generally agree that tan|x| is not periodic, but there is some confusion and differing interpretations about the implications of its graph and symmetry.
Participants reference the need for a clear definition of periodicity and the role of symmetry in determining it, but these concepts remain somewhat unresolved in the discussion.
jambaugh said:Plot the graph. Notice that if you erase the coordinate axes you can still see where the origin must lie.
Bassalisk said:I did plot the graph, that's why i got confused. I saw a lot of functions, resembling tan(x). I got the feeling that it was periodic, but actually tan|x| isn't.
jambaugh said:Look at the graph closely. It should have a mirror symmetry around x=0. But notice it is not mirror symmetric around any other point. So you can't shift the graph through a period so it looks exactly the same.