What is a Codomain?

[atom]

I know this question has come up too often but i still do not understand after reading all the explanations in my textbook. Can someone please explain to me? Thanks

[kamil9876]

Perhaps what most people find confusing about Codomains is that Codomains don't really "do" anything interesting in VCE.

Would you consider the function , the same as the function ? For practical purposes yes, but technically (and perhaps this technicality is beyond VCAA themselves), it is not.

[Bhootnike]

From one of my earlier posts :

 i think the co-domain is the set of possible values which may be produced, when the specific domain is applied to the equation. the range is the ACTUALvalues whichare produced. e.g.

if dom was [1,4], and the codomain was [1,10], and your equation is, say, y=x+1, then your range is, [2,3,4,5]. so codomainislike whatmaypossiblybeobtained, whereas range is the actual/obtained values you get when you 'plug' your x-values into the equation.

the codomainthus wont = R whenyouhave: f:[1,2,3,4,5] --> [1,2,3,4,5,6,7,8,9,10], f(x) = x+1

[brightsky]

From one of my earlier posts :

 i think the co-domain is the set of possible values which may be produced, when the specific domain is applied to the equation. the range is the ACTUALvalues whichare produced. e.g.

if dom was [1,4], and the codomain was [1,10], and your equation is, say, y=x+1, then your range is, [2,3,4,5]. so codomainislike whatmaypossiblybeobtained, whereas range is the actual/obtained values you get when you 'plug' your x-values into the equation.

the codomainthus wont = R whenyouhave: f:[1,2,3,4,5] --> [1,2,3,4,5,6,7,8,9,10], f(x) = x+1

pretty much. it is sometimes useful to think of a relation as a mapping between two sets. you start off with one set (arbitrarily called the domain) which contains certain elements, like {1,2,3,4,5,6}. you then map this set to a new set of numbers/elements called the codomain. each element in the first set (domain) is 'paired up' with an element/elements in the second set (the codomain). however sometimes, nay, most of the time, there are elements in the second set which do not get paired up. the set of all values within the codomain which do get paired up we call the range. the ones that don't...well they're just part of the codomain but not part of the range. do you see how the range is always a subset of the codomain?