How do I know what |x-1| = 1 look like on a graph without a graph calculator.
Is this the proper way of writing it:
$$ \begin{gathered}\begin{gathered}|x-1|=|y|\\ |y|=\begin{cases}y,&y\geqslant 0\\ -y&y<0\\ &\end{cases} \end{gathered} \\ \end{gathered} $$
Or
$$ |x-1|=1=\begin{cases}x=2&x\geqslant 0\\ -\left( x-1\right) =1&x<0\\ &\end{cases} $$
Or
$$ |x-1|=\begin{cases} x-1, \quad x \geq 1\\[2ex] 1-x, \quad x<1 \end{cases} $$
I was told this is the way to write it, but what happens to the ” = 1”? Why do we have x≥1 and x<1? I just wanted to write it in terms of cases, but I don't know how to determine how it looks like on a graph from there.