Answer
(a) See graph (red).
(b) domain $\{x|x\ne1\}$, range $\{y|y\ne5\}$.
(c) vertical asymptote $x=1$, horizontal asymptote $y=5$.
Work Step by Step
(a) To obtain the graph of $y=\frac{1}{x-1}+5$ from $y=\frac{1}{x}$, shift the curve 1 unit(s) to the right, then 5 units up. See graph (red).
(b) We can find the domain $\{x|x\ne1\}$, range $\{y|y\ne5\}$.
(c) We can identify the vertical asymptote $x=1$, horizontal asymptote $y=5$.
