Graph the piecewise defined function:



  x| y
-------
 -3| 3  <--use f(x)=|x|
 -2| 2  <--use f(x)=|x|
 -1| 1  <--use f(x)=|x|
  0| 0  <--use f(x)=|x|
0.5| 0.5  <--use f(x)=|x|
0.9| 0.9  <--use f(x)=|x|
  1|-3  <--use f(x)=x-4 
  2|-2  <--use f(x)=x-4
  3|-1  <--use f(x)=x-4
  4| 0  <--use f(x)=x-4
  7| 3  <--use f(x)=x-4

Plot those points and connect them. The function is discontinuous
at x=1.  It does not include (1,1) but does include points very
near it on the left.  It includes (1,-3) and points right of it 
but no points very near it on the left.  So we draw an open circle
at (1,1) to show that the graph does not include that point. We
draw a closed (darkened) circle at (1,-3) to show that the graph
does include that point: 

 

Edwin