Question about the definition of functions

[vaazu]

Homework Statement

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

Homework Equations

what do the :y mean? I doubt that means divided by y that's why I want to know what does it mean?

The Attempt at a Solution

 

[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'.

 

[HallsofIvy]

Homework Statement

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

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.

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

Homework Equations

what do the :y mean? I doubt that means divided by y that's why I want to know what does it mean?

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

The Attempt at a Solution