# How to graph modulus function graphs

I tried to find out a way to calculate the graph for multivariable modulus functions(eg. $$|x|+|y|=1+x$$)

in this case made a table to find out all possible cases like:

$$y$$/$$x$$ $$x > 0$$ $$x < 0$$
$$y > 0$$ $$y = x$$ $$y = 0$$
$$y < 0$$ $$x = 0$$ $$R$$

On graphing this equation it gives .
I would like to know where i went wrong in this method and is there any better method to draw the graph by hand.

You're table is wrong, it should be

y/x x $$\geq$$ 0 x < 0
y $$\geq$$ 0 y = 1 y = 1 + 2x
y < 0 y = -1 y = -1 - 2x

You can find the formulas for each cell by using the fact that for $$x<0, |x|=-x$$ and for $$x\geq 0, |x|=x$$. Substitute this relation for $$x,y$$ for each cell.

Since LHS is nonnegative, we know that $$x \ge -1$$.

Also, we know from $$|y|$$ that the function must be symmetric about the $$x$$-axis, hence we can focus on $$y \ge 0$$ and then reflect it.

If $$y \ge 0$$ and $$x \ge 0$$, then the equation becomes $$|x|=x$$, and hence our function becomes $$y=1$$.

If $$y \ge 0$$ and $$x < 0$$, then $$|x|=-x$$, and hence $$y=2x+1$$.