Say I'm in state q5 with the following input:
000[q5]100
I'm about to read in a 1 and my instructions are 1->x,L while moving to q6
Would the tape then look like this?
00[q6]0x00?
I'm not sure what to do when reading something from the right but having to move left and the textbook I'm using isn't very descriptive of this process.
In all definitions of TMs that I have seen, the transition function / relation tells you what you should insert instead of the symbol that was just read (which is the one right to the read/write head). Thus you are right,
la[p]br
will turn into
l[q]acr
if there is a transition from p to q defined by b->c,L.