|y| = x + 1

Since |y| ≧ 0, x + 1 ≧ 0, hence x ≧ -1, so we cannot use any values
of x less than 1. 

So we get a few points.

When x = -1 (the smallest value x can take on) 
   |y| = -1 + 1
   |y| = 0
     y = 0, so we have the point (1,0) as the left-most point on the graph.

When x = 0,
   |y| = 0 + 1
   |y| = 1

There are two values of y that satisfy that, 1 and -1,
   so we have the two points (0,1) and (0,-1)

When x = 0,
   |y| = 0 + 1
   |y| = 1

There are two values of y that satisfy that, 1 and -1,
   so we have the two points (0,1) and (0,-1)  

When x = 1,
   |y| = 1 + 1
   |y| = 2

There are two values of y that satisfy that, 2 and -2,
   so we have the two points (1,2) and (1,-2)

That's enough.

We plot what we have:

 

Then draw the graph:



Edwin