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

Domain: $x \in \mathbb{R}$, $x \ne 1$.
Range: $y > 0$
The graph of $y = \frac{1}{x} ^ 2$ has domain $x \in \mathbb{R}$, $x \ne 0$ and $y > 0$.
$y = \frac{1}{x - 1} ^ 2$ is a horizontal shift of 1 unit to the right, so the new domain is $x \in \mathbb{R}$, $x \ne 1$. The range does not change, so it's still $y > 0$.