Solving Piece-wise Functions: y=|x|+x Graph Explained

[Soaring Crane]

I'm doing a review of fuctions, and a nagging question popped up in my mind after completing this problem.

After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values.

I did graph it; it was simple (following is a sketch without values):
------------/
-----------/
_________/

Now the final answer included } y = 0, where x<and=0, and y = 2x, where x>0. I found the equations by looking/calculating the slope for each separate piece. However, what I do not understand is why is it x>0 INSTEAD of x>AND=0 for y = 2x. This is perhaps trivial and easy, but I don't comprehend the reason.

Thanks for your patience.

 

[TD]

Since y = 0 for x = 0, it seems to me that you could include 0 in either of the two functions.

 

[HallsofIvy]

It doesn't matter which side you put x=0 into since the function is continuous at 0.