What is a function? | Functions and their graphs | Algebra II | Khan Academy

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  • čas přidán 5. 06. 2013
  • Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/alge...
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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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Komentáře • 1,1K

  • @ingerfie291
    @ingerfie291 Před 7 lety +3298

    I khan't function

  • @Revilo1
    @Revilo1 Před 7 lety +3612

    Who else is watching the day before their test

  • @georgefan2977
    @georgefan2977 Před 7 lety +1401

    He has taught me more in 3 months that my school in a year.

    • @blakesteenrod4765
      @blakesteenrod4765 Před 4 lety +8

      XenoTek 444 which school are you going to? The teachers sound bad

    • @ok-ws5ge
      @ok-ws5ge Před 4 lety +42

      @@blakesteenrod4765 asking people where they go to school is creepy and odd/weird

    • @edwardguillen4381
      @edwardguillen4381 Před 4 lety +13

      pay more attention then

    • @nestoons4539
      @nestoons4539 Před 3 lety +2

      Luffy it was a rhetorical question

    • @celestialorb1680
      @celestialorb1680 Před 3 lety +5

      @@edwardguillen4381 Thats not how it works idiot people often pay more attention when there teachers are better and make thing more intresting.

  • @utahnash
    @utahnash Před 7 lety +1805

    You know whatd be great. If my teacher taught me like a normal one.

    • @Alyssa-qk8kf
      @Alyssa-qk8kf Před 7 lety +16

      does yours teach from an iBook too?

    • @parriscrowder8356
      @parriscrowder8356 Před 7 lety +13

      I know right teachers these days

    • @utahnash
      @utahnash Před 7 lety +69

      Legit my teachers like heres our topic, heres your vocab... Search both of them online and teach yourself... But she gives us problems to do, but we dont know what to do. Its pretty much heres paper, play on your phone the whole hour.

    • @utahnash
      @utahnash Před 7 lety +26

      Im in 8th grade and sometimes the equations she gives us dont make any sense

    • @bigchef608
      @bigchef608 Před 7 lety +4

      Nash Hansen mine is pretty fun

  • @arjunkaralkar4595
    @arjunkaralkar4595 Před 6 lety +347

    6:12
    _Randomly draws a circle with a mouse._
    *Viewers faint.*

  • @jakolantrn33
    @jakolantrn33 Před 10 lety +774

    how does he write neat using his mouse?

  • @imaudreydriscoll
    @imaudreydriscoll Před rokem +60

    this helped me out a ton. my math teacher doesnt explain this topic very well so i have been struggling in class. i really appreciate this lecture!

  • @Slimssx
    @Slimssx Před 3 lety +494

    Who’s watching this for their online work

  • @mrdude3v
    @mrdude3v Před 8 lety +240

    h(a)h(a) that's pretty funny Sal!

    • @nadiasouilah3425
      @nadiasouilah3425 Před 5 lety +1

      Bray Knapp your ugly

    • @dammitcarl1082
      @dammitcarl1082 Před 5 lety +10

      @@nadiasouilah3425 His ugly what?

    • @syedafarhanasharmin9763
      @syedafarhanasharmin9763 Před 5 lety +5

      @@nadiasouilah3425 you should look at a mirror before calling someone ugly mate

    • @werock5398
      @werock5398 Před 5 lety +5

      @@syedafarhanasharmin9763 the thing is when she looked in the mirror it cracked into a million pieces and cried out in agony

    • @angelstarfire
      @angelstarfire Před 5 lety

      Lol

  • @TheAwesomeAnan
    @TheAwesomeAnan Před 10 měsíci +23

    Thank you for making this app! I am 13 and I really enjoy learning math, science, etc. Khan Academy has really made the process of learning fun, and super interesting. I'm still in shock that such an amazing education platform is completely free!! I am very excited to learn more in the future...once again, thank you so much for Khan Academy.

  • @SaraphL
    @SaraphL Před 11 lety +92

    This is also very useful for beginner programmers, when you say "y = sin(x)", you're actually calling a function sin() with parameter x and overwriting variable y with the result of this function.

    • @themilkman8034
      @themilkman8034 Před 2 lety +2

      True lol I didn't understand functions initially when I learned them in school then I learned how to code and now the topic of functions in math class is super intuitive

    • @zenu903
      @zenu903 Před 2 lety +1

      I've had this epiphany myself when failing to learn how math functions work, turns out they are just like programming functions, which I already understand.

    • @Jee2024IIT
      @Jee2024IIT Před 2 lety +1

      Right,I was in 9th when I learnt how to create functions in python and in 11th our maths teacher taught about functions . Everybody was so confused except me who was thinking what's new in it? lol

    • @defaultset
      @defaultset Před rokem

      @@Jee2024IIT Weird huh? I personally think most programming teachers are better at teaching coding concepts than math concepts, I think it's because programming shows your hard work by running your program whereas math usually does not. Math teachers expect you to just know these things while beginner to intermediate coding teachers assume you don't know so they keep reiterating the definitions. Just my take.

    • @Jee2024IIT
      @Jee2024IIT Před rokem

      @@defaultset So what do you mean afterall,I don't understand the point of your comment

  • @lackadaisicaldreamer
    @lackadaisicaldreamer Před 8 lety +193

    He has such a soothing voice lol

    • @natalyaschulze1039
      @natalyaschulze1039 Před 8 lety +8

      +ChipsAhoy ASMR xD

    • @bellaro-
      @bellaro- Před 6 lety +1

      He repeats so many words.

    • @kekakistuff
      @kekakistuff Před 3 lety

      @@bellaro- wdym?

    • @ST4RZ824
      @ST4RZ824 Před 2 lety

      no i was watching one of the videos and heard him read the word problem and say mmmmm so good

  • @successfulbuild
    @successfulbuild Před 11 lety +25

    I like how he pointed out y = f(x) = x+1, which I've found helps students mentally think of what the new notation means by relating it to something they already know.

  • @biird-7232
    @biird-7232 Před 4 lety +71

    This stuff is really helping in quarantine!! I’m in grade 10 and my teacher assigned a bunch of functions, something that’s entirely new to me. So this is great lol

  • @dangk1334
    @dangk1334 Před 6 lety +87

    when you were high af during this lesson was taught so you have to watch this and try to understand it before the test

  • @mythbuster1133
    @mythbuster1133 Před 6 lety +10

    Simply brilliant. Been trying to draw out the core of this math concept but I usually get confused. . . Until now. Greetings to the KHAN 😊

  • @sirtimbo2924
    @sirtimbo2924 Před 3 lety +8

    This video made me really understand what a function is. Thank you!

  • @chattycarson
    @chattycarson Před 2 lety +7

    I wish my professor taught math the way you do. This made functions so simple.

  • @anniesizemore3344
    @anniesizemore3344 Před rokem +2

    I'm self studying math and just got James Stewart's Calculus today. This video makes functions easier to understand.

  • @riyagurav2592
    @riyagurav2592 Před rokem +2

    and finally I understood the concept!! A big thank you honestly!

  • @Mac-eg5fv
    @Mac-eg5fv Před 7 lety +425

    And then Satan said, "I have an idea, let's put numbers in Math!"

  • @mohammadabbas8458
    @mohammadabbas8458 Před 3 lety +5

    Great lecture , I understood each and everything. 👍

  • @gustavowoltmann9647
    @gustavowoltmann9647 Před 7 lety +6

    It's very good explanation of a function. I like these useful videos.

  • @woohwison3296
    @woohwison3296 Před 3 lety +15

    Hello, everyone. This is a good lecture. This is a good lecture. Everyone, you were born into a good world. And we should thank the people involved in the Cannes Academy. Because their efforts are great. And we have to be careful not to get a corona just like the efforts we make.

  • @Yam-jt3vw
    @Yam-jt3vw Před 4 lety +69

    "... the next larger number that starts with the same letter as a"
    me: *bruh*

    • @psun256
      @psun256 Před 3 lety +3

      mfw you need to pay attention in english to do well in math class xd

  • @jam001420
    @jam001420 Před 11 lety +3

    I love watching him explain. I probably would of done far better if I had this growing up.

  • @cerealman2751
    @cerealman2751 Před 5 lety

    We were using these videos in class and it really helped me, but it didn't help everyone else in my class so he stopped using it and I'm confused again. This helped, thanks.

  • @hodayaifrach9637
    @hodayaifrach9637 Před rokem +2

    this actually helped me understand it better, thank you.

  • @dominicheywood2286
    @dominicheywood2286 Před 4 lety +3

    I think I get this so a function is defined as like a machine where any number placed as an input value will get a substitute output valvue . For e.g
    If I have an operation along with the function
    F(x)= x + 2 where if I put x as being 1 then when included into the function I get the result of 1 + 2 = 3 .

  • @Victoria-lu3or
    @Victoria-lu3or Před 6 lety +180

    I’m still confused...

    • @Kh4lidz
      @Kh4lidz Před 6 lety

      I just want to know one thing, What class is this video for ? How old are you to study this ?

    • @Victoria-lu3or
      @Victoria-lu3or Před 6 lety +13

      Kh4lidz algebra 1, freshman in high school.

    • @paritoshagarwal8840
      @paritoshagarwal8840 Před 6 lety +4

      Kh4lidz this video is for people aged around 15-16

    • @Victoria-lu3or
      @Victoria-lu3or Před 6 lety +7

      Paritosh Agarwal I’m an 8th grader and I am in Algebra 1.

    • @tuksc
      @tuksc Před 5 lety +6

      This is Algebra 2, gotta make sure you went through Alg 1 first lol

  • @casandrarajnarain1314
    @casandrarajnarain1314 Před 5 lety +1

    i would just like to thak you so much , i wouldnt have scored good on my applied maths paper if it wasnt for you. i am so grateful. god bless you

  • @arimbang6798
    @arimbang6798 Před 6 lety

    I could never understand my math teacher at all when he taught this to our class. Now I finally understand THANK YOU

  • @TheEujay29
    @TheEujay29 Před 6 lety +5

    hi sir thanks for your video.
    i have some queries with regards to the book i have read online because i cant understand how they get the values in the example. (see below)
    Ex:
    Let g(x) be the slope of the line tangent to the graph of y=f(x) at the point (x,f(x)).
    a. Estimate the values g(1), g(2), g(3)
    tangent point: (1,0), (2,2), (3,1), (5,-1)
    Solution: y=f(x) with several tangent lines to the graph of f, we can estimate that g(1) (the slope slope of the line tangent to the graph of f at (1,0)) is approx. equal to 1.
    Similarly,
    g(2) approx equal to 0 and
    g(3) approx equal to -1

  • @josephhiatt9959
    @josephhiatt9959 Před 4 lety +3

    First time watching a Khan Academy video (for personal understanding, not because of the kids).
    I'm sure it wasn't intentional, but I enjoyed when he solved f(2) = 3 incorrectly. It gave me an opportunity to prove to myself I understood by personally correcting his mistake before he did. Great confidence builder; very empowering! lol

  • @hundredpercentbricks559

    I love this. Helped me on my algebra hw.

  • @furqanhameed2139
    @furqanhameed2139 Před 7 měsíci

    In topic simplicity no one can compete you in whole CZcams. Thank you so much

  • @nonya9808
    @nonya9808 Před 11 lety +4

    I find these videos very helpful.
    Thank you Khan Academy

  • @allan9422
    @allan9422 Před 3 lety +6

    just going through this so that i dont find it hard when we go back to school after quarantine

  • @ThomasMayhew2000
    @ThomasMayhew2000 Před 7 lety

    Ah, makes so much more sense now. Thanks!!

  • @urfavnntuna
    @urfavnntuna Před 2 lety

    English is not even my first language I checked the most of the terms on translate but this video helped so much thank you! My teachers speak the same language with me and they didnt teach that good

  • @alancantu2557
    @alancantu2557 Před 5 lety +7

    I’m taking the SAT in December and I forgot how to do these

  • @xenom3176
    @xenom3176 Před 7 lety +6

    honestly I forgot all my math lessons in highschool​! arggh!!!

  • @Forgiven289
    @Forgiven289 Před 3 lety

    I love khan Academy it's getting me through algebra 1

  • @nottommy8008
    @nottommy8008 Před 4 lety +1

    Great video. Really helpful.

  • @tharushadakshaka166
    @tharushadakshaka166 Před 2 lety +5

    It was simple but in my lecture it was entangled. Now i'm fully saticfied with your explanation.
    Thank you sir! 🤗

  • @ashleycortes2054
    @ashleycortes2054 Před 6 lety +32

    Just started school, and the PreAp Algebra 2 teacher gave us homework on the first day 😭

  • @varswe
    @varswe Před 5 lety +1

    Thanks for this great explanation now I Know that what is a function

  • @ammarkhalid8719
    @ammarkhalid8719 Před 3 měsíci

    Khan Academy has made me understand this topic very essily THnx :)

  • @zephyr89s
    @zephyr89s Před 10 lety +5

    Khan Academy Rules
    If I was a math teacher, I would just find all of the KA videos for that days lesson, and play them.
    "Watch the TV class!" "(mumble) watch it!"
    (start doodling on a loose paper)
    "now do your homework"
    "DO IT!"
    (goes back to playing minecraft on computer)

    • @AroAliens
      @AroAliens Před 6 lety +2

      i know i'm 3 years late but dude, you'd get fired from teaching...

    • @gurlgenius11
      @gurlgenius11 Před 5 lety +1

      zephyr89s
      Bingo. I've paid for an online college math course that Sal is going to end up teaching. Sal, please just get college accredited, and I'll take YOUR courses.

  • @bloodykills7509
    @bloodykills7509 Před 8 lety +184

    Jesus Christ, this is brain torture. Make it stop. :'(

  • @MJawadSial
    @MJawadSial Před 3 lety

    Very helpful, especially at the end, Thank You Very Much...👌👌👌

  • @woohwison3296
    @woohwison3296 Před 3 lety +2

    좋은 강의네요

  • @ihatedinonuggets
    @ihatedinonuggets Před 9 lety +10

    Very helpful, but one question. What program does he use here? It would be helpful for me online for math

    • @ItsmeIzanami
      @ItsmeIzanami Před 6 lety +4

      Hey Sharaktor how about you shut up and go get a life

    • @themilkman8034
      @themilkman8034 Před 2 lety

      @@ItsmeIzanami never heard of that program before

    • @ItsmeIzanami
      @ItsmeIzanami Před 2 lety

      @@themilkman8034 uhh that comment was from 3 years ago and the dude I replied to deleted his comment

  • @yenohvlog9826
    @yenohvlog9826 Před rokem +5

    My brain can't function

  • @misafirkullanc4658
    @misafirkullanc4658 Před 5 lety

    Thanks so much i understand very well👍🏻

  • @bareaahmalik238
    @bareaahmalik238 Před 6 lety

    This video helped a lot. Thanks for saving humanity.

  • @itsbelayyyy
    @itsbelayyyy Před 5 lety +22

    Me: Okay, okay. I got it.
    Also me: Where tf did that square root of 3 comes from?!

  • @abhin.p3099
    @abhin.p3099 Před 2 lety +3

    Ooh my gwaad I am gonna stop gaming and start learning

  • @drewabbott2016
    @drewabbott2016 Před 4 lety

    Thank you, sir... much appreciated.

  • @ChiNguyen-bc4kt
    @ChiNguyen-bc4kt Před 2 lety

    Thank you very much very clear to understand and contain all necessary knowledge

  • @mt8462
    @mt8462 Před 4 lety +4

    took me 30 seconds to realize this isn't programming related. My brain flexed to its peak to understand comprehend the first 30 seconds.

    • @thatoneguy7193
      @thatoneguy7193 Před 2 lety

      If you think about it though, they're quite similar

  • @mariaalyssalopez9884
    @mariaalyssalopez9884 Před 6 lety +8

    Is this a function F(X)=X^4? Can you explain me how it is a function

    • @ernestovalverde2394
      @ernestovalverde2394 Před 6 lety

      I think so.
      if x == x:
      return x ^ 4
      This is a function in Python which is practically the same as math judging by this video. It's saying if x, raise x to the 4th. F(X) = X⁴. F(3) = 81. Yeah it's a function. I might be wrong though. This is the first video explaining functions (in mathematics) I've watched...this isn't my account btw. I'm a boy...

    • @joannaathineosmathematics5706
      @joannaathineosmathematics5706 Před 4 lety

      It is for sure and to be specific it's a polynomial function. 4 is the exponent and remains the same. Slope is 1.

    • @joannaathineosmathematics5706
      @joannaathineosmathematics5706 Před 4 lety

      Another good explanation to determine if this is a function or not is to see the relation between the two variables x and f(x) . F(x) is always x^4. For every single and different value of x you get a unique and different value for f(x). It's also an even function because of the exponent 4.

  • @muhammadsharif6249
    @muhammadsharif6249 Před 4 lety

    You helped me alot thanks!

  • @linhgabrielnguyen2952
    @linhgabrielnguyen2952 Před 27 dny

    It is super clear and super easy to understand.

  • @guys-xo1pw
    @guys-xo1pw Před 3 lety +3

    Can we get held back in online school?

  • @nyxfairy6538
    @nyxfairy6538 Před 7 lety +31

    this is so difficult

    • @dittyesq
      @dittyesq Před 7 lety +20

      The first time through, it strains the brain. Watch it a second time and it starts to make sense. By the third time, it should "stick" pretty easily.

    • @redfur7216
      @redfur7216 Před 6 lety +5

      Mental
      Abuse
      To
      Humans

    • @ThatDudeEddiee0
      @ThatDudeEddiee0 Před 6 lety

      At first. But the more you practice these kind of problems and sounding it out in your head, it begins to make sense on how the numbers are occurring

    • @joannaathineosmathematics5706
      @joannaathineosmathematics5706 Před 4 lety

      No worries. Watch it again and again...

    • @St-sz8oh
      @St-sz8oh Před 3 lety

      Richard Smith no

  • @salmael-amin159
    @salmael-amin159 Před rokem

    Great lecture. Thankyou

  • @Leylayeesshh
    @Leylayeesshh Před 2 lety

    I am from azeribaijan.THank you very much teacherrrrr

  • @abutalhamahmud
    @abutalhamahmud Před 9 lety +6

    (y)

  • @kamyar9782
    @kamyar9782 Před 7 lety +11

    What the fuck, my brain can't even function properly because of this lesson.

  • @moicaalim8596
    @moicaalim8596 Před 5 lety

    Thank You. I understand it

  • @anggunsoraccajaya1322
    @anggunsoraccajaya1322 Před 3 lety +2

    thanks my guy your voice is so much better than my boring math teacher

  • @chwibii
    @chwibii Před 7 měsíci +3

    im crying because i cant seem to understand this💀

  • @beserned1347
    @beserned1347 Před 7 lety +44

    Dear x,
    Stop asking us to find your daughter.
    Shes never coming back
    Signed FlyingHippos_Derp

    • @blkbaboon
      @blkbaboon Před 5 lety +10

      Noxtixium this is much better:
      Dear z,
      Please stop asking us to find your x.
      She's never coming back. Don't ask y.

    • @minteew9306
      @minteew9306 Před 3 lety

      You commented on this video 3 years ago just reminding you because you probably forgot you ever made this

    • @beserned1347
      @beserned1347 Před 3 lety +1

      Minteew bruh thanks i was 12 when i did this

    • @lemon-vy3mj
      @lemon-vy3mj Před 3 lety

      :c

  • @kavinkannan8371
    @kavinkannan8371 Před rokem +2

    what I am learning in school: how to divide by 10, Khan Academy: arithmetic sequences

  • @DarthTwilight
    @DarthTwilight Před 2 lety

    This makes perfect sense.

  • @mikey20is
    @mikey20is Před 6 lety +4

    took college calc. and now I now what function means...better late than never !

  • @KarlRuizS
    @KarlRuizS Před 6 lety +8

    Why does he make it so complex and confusing, at the beginning it was fine.
    He should go more slowly.

  • @aroomakhan7256
    @aroomakhan7256 Před 7 lety

    the very best work and greatly help us.

  • @adog3129
    @adog3129 Před 10 měsíci +2

    I know I'm not breaking new ground with this comment but this channel is an incredible resource and it's wonderful that it's free for everyone.

  • @shaundellsolomon4668
    @shaundellsolomon4668 Před 7 lety +24

    At 4:38 f (2)=2 wouldnt it be 3 cuz its x+1?

  • @shivshah525
    @shivshah525 Před 7 lety +4

    maths is very much cool thing !!!!

  • @Ruby--.
    @Ruby--. Před 8 měsíci

    This is actually understandable

  • @abhin.p3099
    @abhin.p3099 Před 2 lety +1

    Thank you, khan academy

  • @minerfreakpvp6954
    @minerfreakpvp6954 Před 7 lety +3

    Doesn't this go towards programming?

  • @ratifiedratty101
    @ratifiedratty101 Před 3 lety +3

    I still don’t get it 😑

  • @alayshaortiz9916
    @alayshaortiz9916 Před 4 lety

    This helped me alot

  • @akhilsankar
    @akhilsankar Před 4 lety

    bravo, nailed that thing.

  • @ahihi2002
    @ahihi2002 Před 7 lety +16

    you need some Milk

  • @itzvoid4689
    @itzvoid4689 Před 8 lety +16

    what the heck

  • @kashafanjum8706
    @kashafanjum8706 Před 6 lety

    Good lecture also see the definition of function "Maths in Desi style"

  • @mahendrasubbu2644
    @mahendrasubbu2644 Před 2 lety

    Absolutely he is 100 times better than my school teacher ....

  • @azi9300
    @azi9300 Před 6 lety +4

    wtf is this? im only in 8th grade and my teacher is making me report this.

  • @6ra9
    @6ra9 Před 6 lety +8

    i'm sorry isn't this kind of simple though? i'm a young person. i understand this

    • @6ra9
      @6ra9 Před 6 lety +2

      oml staph.😂😂 yes i am jesus

    • @ernestovalverde2394
      @ernestovalverde2394 Před 6 lety +1

      ImAnArmy czcams.com/video/Q8KP-9mmz1Q/video.html please stop spamming *"aRmY"* every time you see someone with a profile pic related to it. There's way more Man Utd fans both irl and online yet you never see them behaving like they suffer from autism...

    • @ninadoolam6027
      @ninadoolam6027 Před 5 lety

      i understand it now

    • @amrsalah4
      @amrsalah4 Před 5 lety

      :0 0: not really either I’m really dumb or ur gifted idk

  • @tibyann3391
    @tibyann3391 Před 6 lety

    Thank you!!

  • @mrs.boytlive6158
    @mrs.boytlive6158 Před 4 lety

    Great content!

  • @vbrr6508
    @vbrr6508 Před 6 lety +5

    waste of time

  •  Před 11 lety +1

    In the description could be the URL of where is this video on the khanacademy site.

  • @gpaulatheist
    @gpaulatheist Před 3 lety

    Thank you very much sir .

  • @genersonmaghari8470
    @genersonmaghari8470 Před 6 lety

    Im starting to get interested in this math thing