# What is the domain and range of y= abs(x-1)+2 ?

As for domain, $x$ has no limitations (no fractions, no roots), so the domain of $x : \left(- \infty , + \infty\right)$
The brackets mean $| x + 1 | \ge 0$ so the function as a whole is always greater (or equal) than 2:
Range of $y : \left[2 , + \infty\right)$