[Math] Absolute value graph sketching: $||x-1|-1|$

Question

Where would you start if you were told to plot:

$$||x-1|-1|$$

I looked at just $f(x) = |x-1|$ and noticed that the two equations are: $\pm (x-1)$ for $x \geq 1$ and $x < 1$. Extrapolating then: $\pm(\pm(x-1)-1)$, but how would I know which regions which equation would work for?

Answer 1

1) $y=|x|$

2) $y=|x-1|$

3) $y=|x-1|-1$

4) $y=||x-1|-1|$