Question #e2f59

1 Answer
Feb 18, 2015

The graph is this:

graph{|x+2|-|x+1| [-10, 10, -5, 5]}

But why?

We have to "open" all the absolute values, so we have to write for which values of x the two arguments are positive or zero.

The first:

#x+2>=0rArrx>=-2#.

The second:

#x+1>=0rArrx>=-1#.

So we have three intervals:

#x<=-2#
#-2<x<=-1#
#x> -1#

So:

In the first interval both arguments are negative or zero and the function becomes:

#y=-x-2+x+1rArry=-1# an horizontal half-line.

In the second interval, the first is positive and the second is negative or zero and the function becomes:

#y=x+2+x+1rArry=2x+3# a segment.

In the third both arguments are positive or zero and the function becomes:

#y=x+2-x-1rArry=1# another horizontal half-line.