The curve is below.

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.

Note that,

f1=|x| is continous everywhere,

f2=x-1 is continous everywhere,

Thus,

f1 o f2=|x-1| is continous everywhere, (by composition rule).

Thus,

(f1 o f2)+f2=|x-1|+x-1 is continus everywhere, (by addition rule of continous functions).

Thus,

to find the limits of f=|x-1|+x-1

All we need to is evaluate the function at those points.