How to sketch $xyz=0$ near zero

Question

Given set $M=\{(x,y,z) \ | \ xyz=0\}$ how do I go about sketching $M$ near zero. I can't wrap my head around what it should look like. Any help would be great.

Answer 1

The condition $xyz = 0$ is equivalent to $x = 0$ OR $y = 0$ OR $z = 0$. Do you know how to sketch $\{(x,y,z) \ | \ x = 0\}$, $\{(x,y,z) \ | \ y = 0\}$, and $\{(x,y,z) \ | \ z = 0\}$ separately? $M$ is just the union of those sets.