# How do you graph y = 1 + |x-1|?

$y = 1 + x - 1 = x$, for $x \ge 1$ and
$y = 1 - \left(x - 1\right) = - x + 2$, for $x \le 1$
$y = x \mathmr{and} y = - x + 2$, meeting at (1, 1). y=1 bisects the pair.