Answer
(a) See graph.
(b) B $(-\infty,1)U(1,\infty)$, $(-\infty,1)U(1,\infty)$
(c) $x=1$, $y=1$
Work Step by Step
(a) To obtain the graph of $R(x)=\frac{1}{x-1}+1$ from $y=\frac{1}{x}$, shift the curve 1 unit to the right, then shift 1 unit up. See graph.
(b) Based on the graph, we can find the domain as $(-\infty,1)U(1,\infty)$ and range as $(-\infty,1)U(1,\infty)$
(c) We can identify the vertical asymptote $x=1$, horizontal asymptote $y=1$, or oblique asymptote $none$.