# Graph transformation problem

• Aug 7th 2012, 01:09 PM
Frederick
Graph transformation problem
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.
• Aug 7th 2012, 01:19 PM
emakarov
Re: Graph transformation problem
Consider separately x >= 0 and x < 0 and replace |x| by its definition.
• Aug 7th 2012, 01:25 PM
ebaines
Re: Graph transformation problem
You can rewrite the equation like this:

$y = \frac {3x+ |x| } x = 3 +\frac {|x|} x$

The value of $\frac {|x|} x$ 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