It's just like

which is ALMOST the same as the line y=x+2, but has a hole in it at x=2, since you cannot have a zero in your denominator.

In order to make f(x) continuous you plug in x=2 into x+2, giving you 4, filling in that hole.

is not defined along the line y=x.

Everywhere else it is equal to

IF you let y=x, then x+y becomes 2x, or 2y along that line.