Graphing techniques

Compare the original rules $y=2+c/(x-1)$ for $c=5$, $c=-5$ and $c=0$, retaining $x\ne1$ in every case. Before graphing, predict the side of $y=2$ on which each branch lies, the behaviour near $x=1$ and the intercepts. Use a wide view and a close view near $x=1$, then explain which features your screen supports and which require the algebra. For $c=0$, decide why an excluded point remains even though there is no unbounded branch.