There is this question that asks to draw the graph of $|x|+|y|=1+x$ and $y+|y|=x+|x|$. I know how to draw the graph of $y=\ldots$ using elementary techniques of translating, dilating, etc. But this time it is not that straightforward besides by plotting the points one by one and then guess the shape.
Is there any other way besides plotting some points then guess the shape or using any computer to draw the graph?
Many thanks! Helps are greatly appreciated.
Divide into four cases; $(x,y)$ in first, second, third and fourth quadrant, you will get your graph. With this particular question, you will be getting some easy equations.
Regarding the use of $techniques$ you were looking for, here also it can be applied, but becomes a bit tedious. Sometimes its better to use the old school method. Presence of both $|x|$ and $|y|$ in the expressions is always a hint to go old school.