Answer
Domain: (-∞, 1) U (1, ∞)
Range: (-∞, 0) U (0, ∞)
See graph below, green graph is the answer.
Work Step by Step
The question asks for a graph of the function and the function's domain and range.
Given $r(x) = \frac{1}{x-1}$
From $\frac{1}{x}$, the graph is transformed one unit to the right
The vertical asymptote is at x= 1, so the domain is (-∞, 1) U (1, ∞)
The horizontal asymptote is at y = 0, so the range is (-∞, 0) U (0, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{1}{x-1}$