Domain, Codomain, and Range (Correction)

As part of the college algebra series, this video explains the differences between codomain and range, and defines the domain of a function. Chloe gives examples identifying all three.

[muhammadqasim]

Very well explained. The idea of explaining codomain using Venn diagram and the use of Quadratic function made it crystal clear to understand the difference between codomain and range. Thank you !

[Troglodyte]

what's the use of codomain after we know the range already? What is the motivation for this concept?

[Hazellites]

Cleared up years of confusion. Hahahaha thanks.

[HeadphoneTarnish]

First off, given the definitions given in this video, it seems to me that the range can be defined as the minimal codomain- that is, Range = min({A such that A contains the set {f(x) : x is in X}}).

Given this understanding, the codomain is a set that includes the range as a subset and possibly additional points that the domain is not mapped to under the function. What interest is the codomain to us then? Is it simply to tell us what kind of set we are mapping into (e.g. the real plane versus the integers), or does it give us some other information about the function?

Thanks for the video!

[PrincessSakuno]

OHMYOGD THANK SUCH A GREAT EXPLANATION

[wiggasknow]

How is the codomain of x^2 all real numbers if codomain concerns output? How can x^2 give anything less than zero????

[alanp]

But....what's the point of the co-domain? I get that it's basically the possible output of the function but all of the examples you've shown all have the co-domain of ℝ. Are there times when the co-domain isn't just ℝ?

[josephameh]

For f(x) = x^2, what happens to when x=0 so the range is not just positive real numbers but including 0

[agustinbalmaceda]

I like how she looks like is speedrunning the lecture.

[pretty_ok]

Are functions like f(x)=2x or f(x)=x^2 limited to Real numbers for convenience? Isn't it possible to use complex numbers as x?

[atikmahbubtanjim]

Why only normal number become the domen of 3rd example

[maxwellspiano]

I would appreciate it very much if you answer this question: a codomain is the possible outcomes and the range is all the outcomes when the input is a natural number?

[shlovaski]

last example should be from 3 to positive infinity

[botswanastan]

Isn't the domain of x^2+3 minus infinity to positive infinity????

[allanhenriques]

I feel like the easiest way to differentiate range and codomain would be to say,
-codomain is where all elements x in A map to some element(s) f(x) in B,
-whereas for a range, each element x in B maps to element(s) in A, and each element in A maps to some element in B

[angelopedralvez]

The range is a subset of codomain with the same given function😊

[thedeathofbirth]

Wow! This person doesn't even know the difference between natural numbers and whole numbers! And she teaches in a college! Mathematics is about precision!

[nishakarandikar]

In second example range includes not only positive real numbers but also zero.

[emilywong]

Who is the lecturer and where is she from? What level are this lecture?

[suchandraac]

Will the domain and the co-domain always be equal?