# Question about the definition of functions

1. Jan 14, 2008

### vaazu

1. The problem statement, all variables and given/known data
Y={y:y=f(x), xe(can´t find the right symbol, but it should be belongs)X} is the changing region (is it like that in English?) of the function f

function f-s graphic is a region of points in the xy plane is defined as (f)={(x;y):y=f(x),x e X0
2. Relevant equations
what do the :y mean? I doubt that means divided by y thats why I want to know what does it mean?

3. The attempt at a solution

2. Jan 14, 2008

### Dick

Your definition in english reads, Y is equal to the set of all y such that y=f(x) for x an element of X. The ':' is the 'such that'.

3. Jan 14, 2008

### HallsofIvy

Staff Emeritus
Your set is the set of all possible y values. The English term is "range" of f. In "higher mathematics" that might be called the "image" of whatever the domain (values of x) is.

You used it in your first set! It mean "such that". Often a vertical line "|" is used to mean the same thing.