Question

Construct the graphs of the following functions.
$y=(|x+1|-|x-1|)/2.$

Answer 1

$|x+1|$ has $2$ cases when $x>-1$ and $x<-1$

similarly $|x-1|$ has 2 case when $x>1$ and $x<1$

therefore total cases are $x<-1$, -1<x<1, x>1$

in first case equation becomes $\left[\right(-x-1)-(-x+1\left)\right]/2=-1$

in second case equation is =$\left[\right(x+1)-(-x+1\left)\right]/2=x$

in 3rd case eqn=1

therefore the graph is -1 when x<-1, x when $-1<x<1$ ,1 when $x>1$