Question

Write the function f(x)=|2x+1|+|x-2| as a piecewise function without absolute value signs.

Answer 1

Plan:

1. Identify intervals where (2x+1)>=0 and where (2x+1)<0. Same for x-2.

This defines 3 intervals: both expressions are negative, one is negative the other positive, both positive.

2. For each of the intervals evaluate the expressions inside the absolute value and simplify. (I.e. if 2x+1<0 write -2x-1 for |2x+1|.

Summarize by writing something like