The function $f(x)=1/(x-2)$ is discontinuous at $x=2$.The expression $1/0$ is meaningless, so we take the domain to be $A=\{x\in{\mathbb{R}}:x\neq 2\},$ and abbreviate this by writing

and as usual the codomain is ${\mathbb{R}}$. Here $x=2$ is an asymptote, and $y=0$ is an asymptote as $x\rightarrow\infty$.