------------------------------
..............|...............
..............|...............
..............|...............
..............|...............
..............|...............
y = f(|x|) = f|x| (not a fan of this notation outside of logarithms, but that's me)
............./|\.............
............/.|.\.............
.........../..|..\............
........../...|...\...........
........./....|....\..........
--------/-----------\---------
\....../......|......\....../.
.\..../.......|.......\..../..
..\../........|........\../...
...\/.........|.........\/....
..............|...............
Hopefully this has cleared up all the confuzzlation.