Relations and functions | Functions and their graphs | Algebra II | Khan Academy

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Relations and Functions
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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Пікірлер: 532

  • @nanamikents1760
    @nanamikents17603 жыл бұрын

    istg i feel stupid during quarantine. online class aint teaching me anything at all

  • @shayuh1244

    @shayuh1244

    3 жыл бұрын

    Same

  • @onepunchman5033

    @onepunchman5033

    3 жыл бұрын

    Same

  • @heatproof5486

    @heatproof5486

    3 жыл бұрын

    @@shayuh1244 same

  • @mekshek7359

    @mekshek7359

    3 жыл бұрын

    Same

  • @23deepakiyer76

    @23deepakiyer76

    3 жыл бұрын

    same

  • @scottysgamingchannel2259
    @scottysgamingchannel22595 жыл бұрын

    You just made 1 hour worth of babbling from my professor clear in less than 7 minutes, thank you.

  • @heavensent9173

    @heavensent9173

    4 жыл бұрын

    call proff mr babylonian

  • @elronmernilogaming543

    @elronmernilogaming543

    3 жыл бұрын

    True

  • @MZKI201

    @MZKI201

    3 жыл бұрын

    fax

  • @marimari09

    @marimari09

    3 жыл бұрын

    @KSKCC-9 Besson wait a minute

  • @soupymeow

    @soupymeow

    3 жыл бұрын

    Did you fail?

  • @Abliskarian
    @Abliskarian6 жыл бұрын

    A really easy way I remember whether it's a function or not is if there are more numbers in the range than domain, it's not a function

  • @chawanangwachiponyirenda2808

    @chawanangwachiponyirenda2808

    3 жыл бұрын

    It’s a good one

  • @omransaeed1988

    @omransaeed1988

    3 жыл бұрын

    You mean if there are repeated numbers in the range, it's not a function?

  • @mathematicsfordummy598

    @mathematicsfordummy598

    3 жыл бұрын

    @@omransaeed1988 That is not really the case. The domain or the admissable value of x do not occur more than once. Let's say for example, we have f(x) = x+1. We assume that our x or the domain is 1, then we have the range of 2 or the resulting values of y is 2. The given function x+1 if substituted with the admissable value of 1 will always have the resulting value of 2 which makes it a function. Let us have another example, x^1. Given we have a domain of 1 and -1, the resulting values of both the admissable values of 1 and -1 are both 1. Which makes is a function.

  • @kvuxi5695

    @kvuxi5695

    3 жыл бұрын

    Y’all really smart I’m over here having a mean talk breakdown cause I don’t know anything about math

  • @leilahvillegas2153

    @leilahvillegas2153

    3 жыл бұрын

    @@kvuxi5695 literally me rn on a Sunday night trying to figure out how to do my 4 math assignments due at 11:59 pm

  • @nithinvarma817
    @nithinvarma8178 жыл бұрын

    Why do teachers make every shit complicated.....You are awesome! thanks a lot :)

  • @dankmemer6626

    @dankmemer6626

    7 жыл бұрын

    true though

  • @dankmemer6626

    @dankmemer6626

    7 жыл бұрын

    true though

  • @5injl

    @5injl

    7 жыл бұрын

    LMAOO. TRUE

  • @juanmares8104

    @juanmares8104

    6 жыл бұрын

    Steezy Bois

  • @famestar1065

    @famestar1065

    6 жыл бұрын

    Omfg u are right

  • @atmoak7063
    @atmoak70635 жыл бұрын

    So if X cheats on Y you have a dysfunctional family? *EDIT: After reading other comments I’m really sad that this wasn’t original*

  • @ipotatosenpai7002

    @ipotatosenpai7002

    4 жыл бұрын

    :

  • @Red_Adanac

    @Red_Adanac

    3 жыл бұрын

    so Y did X cheat?

  • @leulyonas3947

    @leulyonas3947

    3 жыл бұрын

    Idk y he did it but is x a woman y

  • @sd0wi100
    @sd0wi1004 жыл бұрын

    For everyone who didn’t understand For example you have (-3,-2),(-2,4),(0,5),(-2,6),(3,8) The domain is always the first number Domain: -3,-2,0,3 Range:-2,4,5,6,8 (FYI- I didn’t add two -2’s because it is mentioned once so you don’t have to add a number more then once) So it will be -3 linked with -2 -2 linked with 4 0 linked with 5 -2 linked with 6 ( again) 3 linked with 8 Therefore it’s not a function because -2 is linked with 4 and 6 so that’s not a function That’s the whole lesson for you Like if this helped ☺️👍🏾

  • @Red_Adanac

    @Red_Adanac

    3 жыл бұрын

    Nice

  • @sebastianhohmannhernandez4046

    @sebastianhohmannhernandez4046

    Жыл бұрын

    Tsym

  • @kingp3rcius283

    @kingp3rcius283

    Жыл бұрын

    Is it applicable for range too??

  • @gameonm8737

    @gameonm8737

    Жыл бұрын

    @@kingp3rcius283 no cause its possible for range to have more than two values. Look at a quadratic function

  • @Perfectiqn

    @Perfectiqn

    Жыл бұрын

    My mom spent 800$ on a school course lesson and I had to sit down for 1 and a half hours just for you to easily explain here

  • @clasher6732
    @clasher67322 жыл бұрын

    You made it very easy to understand, I failed to listen to our 3 day class regarding this lesson and I learned everything I needed to learn in just 7 minutes, I understood every detail that I needed to get to pass my exam, Great video.

  • @tyongtyong4311
    @tyongtyong43113 жыл бұрын

    so basically it's the matter of one member of the domain being loyal to a member of the range for it to become a function. if the member of domain cheats on one member of the range and marries another member of the range, then it's no longer a function.

  • @maricarcunanan321

    @maricarcunanan321

    2 жыл бұрын

    Exactly!

  • @eenyl.3341
    @eenyl.33415 жыл бұрын

    My teacher made this so confusing. Thanks for actually teaching me

  • @minbeomu
    @minbeomu3 жыл бұрын

    *Function:* One to one Many to one *NOT Function:* one to many

  • @reycuevas5378

    @reycuevas5378

    3 жыл бұрын

    Good bro

  • @gamerx3354

    @gamerx3354

    3 жыл бұрын

    Pretty much

  • @zuri4832

    @zuri4832

    3 жыл бұрын

    Still don’t understand

  • @laurenkirbyyyy

    @laurenkirbyyyy

    3 жыл бұрын

    thank you!

  • @mcdonaldsemployee7010

    @mcdonaldsemployee7010

    3 жыл бұрын

    @nattiroo no that would not be a function, if you still need it

  • @Rose-dw2iw
    @Rose-dw2iw5 жыл бұрын

    Man you just saved my life , I hope you to have the best life and thank you thank you thank you so much , my teacher never explains anything I have been having a lot of trouble understanding from her , she's nice but doesn't explain well but you man just made my day and I hope god makes your life the best life and a healthy life too😄

  • @donghyuckismyyeobo6785
    @donghyuckismyyeobo67855 жыл бұрын

    My tiny brain still cant understand anything

  • @gialuie8164

    @gialuie8164

    4 жыл бұрын

    Wellllll me big brain have tiny knowledge

  • @cboyslim5490

    @cboyslim5490

    4 жыл бұрын

    i hope you ended up figuring it out, master big brain

  • @donghyuckismyyeobo6785

    @donghyuckismyyeobo6785

    3 жыл бұрын

    @Gabriel Renovalles I am. Googoo gaga

  • @kwiiba168

    @kwiiba168

    3 жыл бұрын

    @@donghyuckismyyeobo6785 LMFAOOO PLS

  • @horndog5368

    @horndog5368

    3 жыл бұрын

    he's basically saying that you can have multiple numbers in the domain that can mapped in one of the range, but you cant have 1 number in the domain to be mapped into multiple numbers in the range, because as he said it aint a function

  • @amyhetherington4885
    @amyhetherington48853 жыл бұрын

    This is amazing. If only all lecturers could explain like you!

  • @sarahidk7550
    @sarahidk75502 жыл бұрын

    Thanks dude this really helped, missed a few days of school and needed to catch up. :)

  • @jelohsimo2435
    @jelohsimo24353 жыл бұрын

    The way you explained how a function is basically an association in which you KNOW what a certain element of the domain is exclusively associated with the range is actually a pretty good idea I always seemed to doubt whether many-to-one relation is the function or not. Thank you!

  • @crowking7566
    @crowking75665 жыл бұрын

    Thank you so much. I was so stressed out about a problem but you put it into easy, understandable words; now it all makes sense!!!

  • @Katiegetsonyoutube
    @Katiegetsonyoutube3 жыл бұрын

    (see time 4:06) It helps from the beginning if you explain that the "domain" is the first number in each set of parentheses and the "range is the second number. And that when you write out your domain numbers, you write them from negative to positive AND you don't need to write a number twice (like -2). The only way it is a function is if the Domain ARROW points to ONE member of the RANGE. Basically, if anything is pointing to more than one number it's not a function. Boom. there you have it.

  • @marianavm2355

    @marianavm2355

    2 жыл бұрын

    This should be pinned idk why he didn't explain any of this

  • @elronmernilogaming543
    @elronmernilogaming5433 жыл бұрын

    YOU explained it so well... I mean if this is class my teacher is just gonna discuss this for one hour and I can't understand a thing and you made it clear in less than 7 minutes

  • @valromo
    @valromo10 жыл бұрын

    Thanks man...Lol my teacher thought me a weird way to remember this..."X cant cheat on Y" or for domain and range its"D.R XY(D goes on top of the X and R goes on top of the Y)Cool vid

  • @sadparty7807
    @sadparty78075 жыл бұрын

    I’m going to fail this year

  • @ankitaaarya

    @ankitaaarya

    5 жыл бұрын

    Did you failed, any updates?

  • @Notme-dv5xr

    @Notme-dv5xr

    5 жыл бұрын

    Sad Party same I’ve got a test tom and I don’t understand

  • @sadparty7807

    @sadparty7807

    5 жыл бұрын

    Ankit Arya not yet, 3 months left of school

  • @thapeloaobakwekomanyane3621

    @thapeloaobakwekomanyane3621

    5 жыл бұрын

    Try not to @@sadparty7807 . make it happen ok

  • @ikennaoparah7498

    @ikennaoparah7498

    5 жыл бұрын

    I got a test tomorrow and this is helping out a lot I wish the best for you sad party

  • @ellworthacquaye8912
    @ellworthacquaye891210 жыл бұрын

    this is really good. makes learning much easier, thumbs up.

  • @spamacc9621
    @spamacc96214 жыл бұрын

    Why did i not understand this when my teacher gave 7 classes on this and i understood 7 minutes of this video, thank you. You should really be a teacher

  • @S.SortaLiving
    @S.SortaLiving Жыл бұрын

    This lecture coupled with these comments just saved my grade (and my Brain) thanks y’all!!!

  • @Ino20
    @Ino204 жыл бұрын

    This takes alot of weight off my shoulders thank you its alot easier to understand

  • @napoleonn.belano2489
    @napoleonn.belano24895 жыл бұрын

    thanks.. this is our lesson tomorrow so Im just gonna sleep in General Mathematics.. what a relief..

  • @abhin.p3099

    @abhin.p3099

    2 жыл бұрын

    Hey

  • @omransaeed1988
    @omransaeed19883 жыл бұрын

    I have a test next week and my teacher is required to explain in English since our class is an elite class (Meaning we study in English when it's not our native language and it's so hard sometimes) and all of his pronunciation, grammar, vocabulary etc. Is so bad that I do not understand a word of what he says! And when I express that I can't understand? He repeats exactly the same words that I did not understand from... So this is really helpful to me, thank you Khan for making this video! Love from the U.A.E

  • @petekeyism

    @petekeyism

    2 жыл бұрын

    I’m from the UAE too! I have a Mathematics final today and I’m pretty confident in all areas except this one because I was absent when my teacher taught this :(

  • @dehydrated17yroldbitch77
    @dehydrated17yroldbitch773 жыл бұрын

    at first i didn't understand a thing possibly because i read alot of this comments and made me anxious alot but as you finish the video you'll start to understand and learn it all and that was hella great

  • @holdenbrado171
    @holdenbrado1714 жыл бұрын

    Thank you so much I learned something from this vid, I might get honor role once again😀👌

  • @jaida.elised9507
    @jaida.elised95075 жыл бұрын

    very well explained. thank you!!

  • @mikays7059
    @mikays70594 жыл бұрын

    the way this is explained is so simple. thank you very much!

  • @margrette8452
    @margrette84523 жыл бұрын

    Thank you so much!!!! This made my lessons so easy:) better than reading complicated module and a very long discussion!

  • @mai-qn6sl
    @mai-qn6sl3 жыл бұрын

    It’s 2020 and yes I have exam this week pray for me I don’t want to fail🏃🏻‍♀️💨

  • @tsukiru1225

    @tsukiru1225

    3 жыл бұрын

    me too, i have it tmrw and im def failing LMAO gl tho!

  • @tchumiu

    @tchumiu

    3 жыл бұрын

    KSKSKSKSSK I HAVE MATH EXAM TOMOROW SKSKSKSK also where r u from like just which country ik weird question

  • @tchumiu

    @tchumiu

    3 жыл бұрын

    @@tsukiru1225 SLAKDKASKDFKAS SAME r u arab?

  • @tsukiru1225

    @tsukiru1225

    3 жыл бұрын

    @@tchumiu I AM!

  • @tsukiru1225

    @tsukiru1225

    3 жыл бұрын

    @@tchumiu I have an Arabic exam legit- like- RN LMAOAOAOA

  • @brookejones2129
    @brookejones21293 жыл бұрын

    A super way to remember this is that domain is x and range is y. And one domain can’t have multiple ranges

  • @subbysofficialtv2930

    @subbysofficialtv2930

    3 жыл бұрын

    Yes it can but it would just be called a relationship that's not a function

  • @ayushjha2677
    @ayushjha26775 жыл бұрын

    Thank you Khan academy it helped a lot 😃

  • @kennethcain6288
    @kennethcain62887 жыл бұрын

    Please keep Producing more math videos!! Its very helpful!!. Thanks to Khan Academy!! :)

  • @medievalmusiclover
    @medievalmusiclover6 жыл бұрын

    I already watched other videos about this topic, but you have the best guide, teaching style and order that no other publishers have. Excellent Job Khan.

  • @menace275
    @menace2752 жыл бұрын

    This was so useful! Thank you so much.

  • @soerenna
    @soerenna3 жыл бұрын

    you are a great teacher sal, thanks a lot!!

  • @RY-pv8gr
    @RY-pv8gr4 жыл бұрын

    I like this 👍u tell us the simplest way to understand Tnx

  • @alexandradalas531
    @alexandradalas5314 жыл бұрын

    thanks Khan Academy... it helps me a lot!!!!!!!

  • @Sara3346
    @Sara33465 жыл бұрын

    I love your work mate.

  • @ranjerkpids3895
    @ranjerkpids38954 жыл бұрын

    Thank you !My teacher havent teach us bout this, now i understand

  • @honeyypool
    @honeyypool2 жыл бұрын

    My dad is awesome math, but I'm not gonna lie, this is a way better explanation, and English isn't even my first language. Thanks!

  • @Kersploinky
    @Kersploinky3 жыл бұрын

    You just made me pass my algebra class.

  • @chlorox817
    @chlorox8174 жыл бұрын

    i like it how my professor gives out easy examples but whenever tests comes those examples never hepled us

  • @dewantahmid95
    @dewantahmid955 жыл бұрын

    That was useful !

  • @sebbyloml
    @sebbyloml5 жыл бұрын

    thank you so much. You made it so easy to understand.

  • @dondoohzono3466
    @dondoohzono34667 ай бұрын

    simply amazing!

  • @R0kudo
    @R0kudo4 жыл бұрын

    thank you so much!!

  • @madgoldnz
    @madgoldnz12 жыл бұрын

    I Agree with DareDefyMe88 If you don't like it, then why bother watching Sal's videos. All he is doing is helping you. For Free. If you don't understand, you need to go back to more basic stuff then work your way forward. You can't blame your own lack of brains on this generous man's vids.

  • @HannaMeiLevine
    @HannaMeiLevine10 жыл бұрын

    Thank you! This really helped.

  • @UNT1M3LY
    @UNT1M3LY2 жыл бұрын

    Thanku!! I haven't learned this lesson in school yet but i have a friend having trouble and i wabted to help!

  • @kiraferatz1467
    @kiraferatz14676 жыл бұрын

    Thank you for explaining it in a simple way. Appreciate you Khan Academy!

  • @agnesdeleon469
    @agnesdeleon4695 жыл бұрын

    What a great video I LOVE YOU 🎉😍

  • @Ghosttt3
    @Ghosttt39 жыл бұрын

    THANK YOU!!!!!!

  • @francesmedina4387
    @francesmedina43877 жыл бұрын

    Thanm you khan academy! Very helpful video. May God Bless you!

  • @dirtyproductions6865

    @dirtyproductions6865

    7 жыл бұрын

    our lesson in math is also in this kind of topic but i think this lesson is for grade 8? since im already grade 10 but our prof is a senior high school teacher.

  • @t0x1cear34

    @t0x1cear34

    6 жыл бұрын

    Dirty Productions we had this in grade 6

  • @dbmxdarkrider2545

    @dbmxdarkrider2545

    Жыл бұрын

    Hi

  • @k3nny5ijo80
    @k3nny5ijo804 жыл бұрын

    "Big fuzzy cloud looking thing"

  • @theweirdo2187

    @theweirdo2187

    3 жыл бұрын

    😭😭😂😂😂

  • @jazeeljohnt.crescini4500
    @jazeeljohnt.crescini45003 жыл бұрын

    Your voice sounds like the narrator on the scary animated stories im watching well i just notice it hahahaha but the math explanation is worth watching😊

  • @themostjinfullmomentinlife7185
    @themostjinfullmomentinlife71853 жыл бұрын

    Yo this helped a lot, thank you💕

  • @canIgetsubs-mg2zj
    @canIgetsubs-mg2zj2 жыл бұрын

    Thanks i answered my problem

  • @Bigboipeepee6969
    @Bigboipeepee69693 жыл бұрын

    Dude thanks you gonna make me past that test tomorrow

  • @little_a.m.productions1399
    @little_a.m.productions13992 жыл бұрын

    Lots of words on our modules still doesn’t help but this vid helpeddd soo much!

  • @paultidwell8799
    @paultidwell87992 жыл бұрын

    Thanks Khan!

  • @SkxThe
    @SkxThe6 жыл бұрын

    my teacher cant teach this, she rushes lessons and doesn't take any questions. Thanks khan your always there for me. (This is when math actually gets hard)

  • @jeremiefreeworld7927
    @jeremiefreeworld79273 жыл бұрын

    Very Helpful

  • @pmdchi
    @pmdchi2 жыл бұрын

    thakn you, very well explained

  • @nicolelyons7748
    @nicolelyons77482 жыл бұрын

    This is really help full

  • @blizzard4621-
    @blizzard4621-3 жыл бұрын

    Thanks for making this easy

  • @AlySarver
    @AlySarver12 жыл бұрын

    Oh my goodness, thank you so much. I didn't get a clear way of seeing this, now I do. Thank youu !

  • @XanderRei
    @XanderRei3 жыл бұрын

    so you watch this the night before the exam? bloody legend mate

  • @an-lt6io

    @an-lt6io

    3 жыл бұрын

    watching this as i do the exam lmao

  • @zainabamjad5873
    @zainabamjad58733 жыл бұрын

    Awesome ...

  • @bashsusulan2109
    @bashsusulan21092 жыл бұрын

    I finally understand it omfg thanks broooo-

  • @kayleethomas1377
    @kayleethomas13776 жыл бұрын

    Thanks I understand....

  • @_jadenmart
    @_jadenmart4 жыл бұрын

    you made this so simple in under 7 min

  • @Chelsieelf
    @Chelsieelf9 жыл бұрын

    Appreciate this simple, easy to understand lesson :) thanks

  • @xduraaful
    @xduraaful10 жыл бұрын

    thank you!

  • @DaFan86
    @DaFan8612 жыл бұрын

    THAAAAAAAAANK YOU!!! I LOVE YOU MAN!! YOUR BETTER THAN ALL OF MY TEACHERS!

  • @ski34able
    @ski34able3 жыл бұрын

    great video!!

  • @badertube6559
    @badertube65592 жыл бұрын

    Thank you so much

  • @rrrrrrrrr7248
    @rrrrrrrrr72482 жыл бұрын

    Very grateful

  • @ari.p.h
    @ari.p.h2 жыл бұрын

    Thank you so much you are always better than my teacher

  • @ShortL.
    @ShortL. Жыл бұрын

    I missed 1 day of class and apperantly this is what they learnt on that 1 day

  • @sheldonblackwood4483
    @sheldonblackwood44833 жыл бұрын

    Nice video and explanation.

  • @articwolf8377
    @articwolf837710 жыл бұрын

    Thank you so much this was super clear!!

  • @princekumarsingh243
    @princekumarsingh2433 жыл бұрын

    really its so much nice sir,,,,,

  • @haste4671
    @haste46712 жыл бұрын

    Thank you so much you make my life in peace

  • @adrielfeliciano8695
    @adrielfeliciano86952 жыл бұрын

    Thanks so much

  • @5ijlv698
    @5ijlv6985 жыл бұрын

    Thank u 💗

  • @Sherrixo
    @Sherrixo10 жыл бұрын

    Gonna watch all these during my holidays and get ready! Hehe :D

  • @QuotesSpire
    @QuotesSpire6 жыл бұрын

    Thank you so much this really helped 😊🙏🏽

  • @thunayanalshammri2628
    @thunayanalshammri26285 жыл бұрын

    thank you teacher

  • @isaiahhyanez
    @isaiahhyanez7 жыл бұрын

    omg you guys are soooooo helpful my math program (apex) is horrible at explaining things

  • @coconat03
    @coconat035 жыл бұрын

    Thanks a lot :>

  • @omransaeed1988
    @omransaeed19883 жыл бұрын

    Teachers typically spend half the lesson going on a speech like they're going in the elections for president on before actually _teaching_ and your brain automatically stops listening to him and mid speech, he actually begins to teach about the subject he's supposed to teach and your still not listening to him so you miss half the explanation. ):

  • @rustygold4969
    @rustygold49695 жыл бұрын

    Very helpful

  • @namasteeats
    @namasteeats3 жыл бұрын

    amazing explanation

  • @ryo0812ca
    @ryo0812ca12 жыл бұрын

    You deserve a noble prize!

  • @kannan3801
    @kannan380110 жыл бұрын

    Tq very much.i pray for khan academy to reach more heights of success.

  • @mariettamiddlegradesptsa8756
    @mariettamiddlegradesptsa87566 жыл бұрын

    thanks this video helped a lot

  • @damienrodriguez4453
    @damienrodriguez44539 жыл бұрын

    That helped so much