TITLE: What is this notation for a function? I've never seen it written like this before.
QUESTION [5 upvotes]: What does this mean? 
$$ f=\{ (x,y): y= x+2 \}$$
I don't understand what "$(x,y):$" means in regard to the problem. Also why is the $y$ inside of the $f(x)$ function. Isn't it supposed to be outside?

REPLY [2 votes]: If you would have the function (in your usual sense) $f(x) = x+2$, the set $f$ you described above would be precisely the graph of the function. In other words, instead of giving you the value of $f(x)$ for each $x$ (which is indicated by the equality $f(x) = x+2$), you are being given the set of points in the plane which are on its graph, that is, the couples $(x,y)$ such that $y = f(x)$ (i.e. $y=x+2$). 
Hope that helps,