Question

Question #e2f59

Answer 1

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.