Note if your graphing software does not have the absolute value function you can graph y=sqrt(x^2) that is a nice trick to replace it.
To find the limits is very easy.
f1=|x| is continous everywhere,
f2=x-1 is continous everywhere,
f1 o f2=|x-1| is continous everywhere, (by composition rule).
(f1 o f2)+f2=|x-1|+x-1 is continus everywhere, (by addition rule of continous functions).
to find the limits of f=|x-1|+x-1
All we need to is evaluate the function at those points.