Answer
See below.
Work Step by Step
It can be, if it is only defined for that point or in other words, its domain only consists of one number. E.g. $f(x)=3$ if $x=0$ (so the domain only consists of $0$) and $f(x)$ is undefined if $x\ne0$ is an example of a function that only consists of a single point on its graph.
