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initial version

Try this version:

f = piecewise([((-oo,-2), 3*x+1), ([-2,2], 2),((2,oo),3*x+1)], var=x);  
f.limit(x=-2,algorithm='giac',dir='-')

Try this version:

f = piecewise([((-oo,-2), 3*x+1), ([-2,2], 2),((2,oo),3*x+1)], ([-2,-2], 2),((-2,oo),3*x+1)], var=x);  
f.limit(x=-2,algorithm='giac',dir='-')
f.limit(x=-2,algorithm='giac')