Consider separately x >= 0 and x < 0 and replace |x| by its definition.
Graph: (3x + |x|) / x
I don't know how to go about graphing this other than making a table of input and output values. The answer key shows two horizontal lines at y = 2 and y = 4, however, with no values at the actual y axis.
You can rewrite the equation like this:
The value of is +1 for positive x, -1 for negative x, and undefined for x=0 (since the quanitity 0/0 is undefined). So the function becomes: y = 4 for x positive; undefined for x=0; 2 for x negative