Hi,

Im trying to solve a problem from my algebra 2 book having to do with absolute value function graphing. The equation is:

y=|x+1|+|x|

here is the graph:

Graph 1.pdf
What I have done is find both of the slanted lines algebraically, and i found those to be:

y=2x+1 and y=-2x-1.

I did that by splitting the original equation into 2 different positive and negative equations, then simplifying:

y=x+1+x=2x+1

y=-(x+1+1)=-2x+1

I have the feeling i did that prematurely, because i didn't find the domain of each equation.

Basically my biggest question stems from the conceptual perspective. What do you do when there are two absolute value terms in an function and how do you find the individual functions and their respective domains?

Thanks!!