Repeat the defining interval without losing endpoints

$f(1)=3+1=4$. Reduce 8 to 4, which belongs to the defining interval $(0,4]$: $f(8)=f(8-4)=f(4)=7-4=3$. Reduce 29 by 28 to 1: $f(29)=f(1)=4$. Multiples of 4 reduce to 4, not to an undefined base input 0.

Translate the defining two line segments by integer multiples of 4 and clip to $-3<x\le8$. The first endpoint is excluded by the requested sketch interval; the last is included. All interior peaks and troughs are included. Although the base rule excludes 0, the periodic extension defines $f(0)=f(4)=3$. Follow the source remark: label endpoint coordinates and each point where the segments meet.