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

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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!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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[@ingerfie291]

I khan't function

[@noviebaloney]

god dammit dude

[@aieshah8060]

Seriously 😂

[@lurker784]

Get out 😂😂😂

[@believer9541]

😂😂😂

[@maymiller3639]

Lmao

[@georgefan2977]

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

[@blakesteenrod4765]

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

[@ok-ws5ge]

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

[@edwardguillen4381]

pay more attention then

[@nestoons4539]

Luffy it was a rhetorical question

[@celestialorb1680]

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

[@Revilo1]

Who else is watching the day before their test

[@tayloralison3898]

Revilo 366 Me lol. I'm struggling. I don't want to fail.

[@dantesudaria5554]

Revilo 366 bwhahaha 😂😂

[@saltymango8742]

omg yes I'm screwed

[@capt_awesomest1957]

Yes, I have a test tomorrow.

[@bearjordan2081]

me......................................................at 11pm

[@utahnash]

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

[@Alyssa-qk8kf]

does yours teach from an iBook too?

[@parriscrowder8356]

I know right teachers these days

[@utahnash]

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]

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

[@bigchef608]

Nash Hansen mine is pretty fun

[@arjunkaralkar4595]

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

[@agentphantom9076]

he is using pen tablet

[@gabrielsiteny]

Still, impressive

[@stevencooke6451]

That was quite impressive.

[@weirdasff]

@@agentphantom9076 most of us cant even draw that nice with a tablet :/

[@adityansh]

Tablet with Stylus*

[@jakolantrn33]

how does he write neat using his mouse?

[@Cluetube]

i was thinking the same. then i was like "he must have one of those drawing pad things, or he is a artist"

[@zuesr3277]

he uses a bamboo pad

[@disintegratesintobinary655]

tampax

[@aflyingpumpkin1073]

i think he is using a tablet

[@kxminxri]

@@disintegratesintobinary655 oh god

[@SaraphL]

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]

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]

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]

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]

@@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]

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

[@mrdude3v]

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

[@nadiasouilah3425]

Bray Knapp your ugly

[@dammitcarl1082]

@@nadiasouilah3425 His ugly what?

[@syedafarhanasharmin9763]

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

[@werock5398]

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

[@angelstarfire]

Lol

[@Slimssx]

Who’s watching this for their online work

[@KaedeharaKai]

Me

[@KaedeharaKai]

My teacher said 3 functions but we dint study for this

[@blackbirdflightsim495]

meer

[@itsniyah1745]

im guilty

[@red_5687]

Me ;-;

[@imaudreydriscoll]

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!

[@lackadaisicaldreamer]

He has such a soothing voice lol

[@natalyaschulze1039]

+ChipsAhoy ASMR xD

[@bellaro-]

He repeats so many words.

[@kekakistuff]

@@bellaro- wdym?

[@ST4RZ824]

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

[@TheAwesomeAnan]

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.

[@Mac-eg5fv]

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

[@walter4609]

Your Average Savage do you mean letters

[@windowpane7841]

Mac *letters

[@zoebradshaw9246]

Mac *letters in math

[@jehieljoseph1220]

U mean letters...annoying asf

[@troupemember1474]

This comment had potential for greatness

[@successfulbuild]

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]

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

[@mila6731]

Me too haha, except I’m doing 8th grade math

[@buzzpus7407]

Same

[@lollyteddybear1357]

Me too except I'm doing 7th grade math

[@indestructible247]

i am learning this in the ninth grade

[@kettlebellsandcoffee]

@@indestructible247 I am doing it in 10th though I learned about it 8th (I just forgot Lol)

[@dangk1334]

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

[@Yam-jt3vw]

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

[@psun256]

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

[@chattycarson]

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

[@sirtimbo2924]

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

[@mythbuster1133]

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

[@Victoria-lu3or]

I’m still confused...

[@Kh4lidz]

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

[@Victoria-lu3or]

Kh4lidz algebra 1, freshman in high school.

[@paritoshagarwal8840]

Kh4lidz this video is for people aged around 15-16

[@Victoria-lu3or]

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

[@tuksc]

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

[@gustavowoltmann9647]

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

[@anniesizemore3344]

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

[@riyagurav2592]

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

[@mohammadabbas8458]

Great lecture , I understood each and everything. 👍

[@jam001420]

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

[@arimbang6798]

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

[@cerealman2751]

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.

[@woohwison3296]

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.

[@allan9422]

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

[@casandrarajnarain1314]

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

[@hodayaifrach9637]

this actually helped me understand it better, thank you.

[@TheEujay29]

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

[@ashleycortes2054]

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

[@bushrasmk321]

ashley Cortes same here we start taking quiz first week of school 🤒🤧

[@Juliana-sy6vp]

ashley Cortes same here omgggggg

[@fireychaos6615]

Same here mate , I shall suffer with you.

[@joannaathineosmathematics5706]

Algebra 2 lucky you!!!

[@kavinkannan8371]

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

[@adog3129]

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.

[@zephyr89s]

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]

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

[@gurlgenius11]

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.

[@dominicheywood2286]

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 .

[@furqanhameed2139]

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

[@ThomasMayhew2000]

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

[@xenom3176]

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

[@alancantu2557]

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

[@hundredpercentbricks559]

I love this. Helped me on my algebra hw.

[@varswe]

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

[@itsbelayyyy]

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

[@aaimalkhankhattak]

kzbin.info/www/bejne/b2HHmYugm5uLb5o

[@nonya9808]

I find these videos very helpful. Thank you Khan Academy

[@urfavnntuna]

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

[@moigabriel4684]

His handwriting with the mouse is so impressive you can just tell this man’s a pro

[@abhin.p3099]

Ooh my gwaad I am gonna stop gaming and start learning

[@mt8462]

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]

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

[@ChiNguyen-bc4kt]

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

[@Forgiven289]

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

[@yenohvlog9826]

My brain can't function

[@peakyblinders1651]

Can't agree more

[@ihatedinonuggets]

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

[@ItsmeIzanami]

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

[@themilkman8034]

@@ItsmeIzanami never heard of that program before

[@ItsmeIzanami]

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

[@nottommy8008]

Great video. Really helpful.

[@anggunsoraccajaya1322]

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

[@josephhiatt9959]

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

[@bloodykills7509]

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

[@leilaniwilson2968]

That is not nice to say that boy 😫😫😫😫😫😫🌋🌋🌋🌋🌋🗻🗻🍾

[@joannaathineosmathematics5706]

😂😂 Well gotta be honest is not that difficult when you hear it from him

[@tylerjones8232]

Wrong

[@TF-cy9ei]

@@tylerjones8232 yea it is i dont understanddd

[@blackstorm8716]

from 6:29 i didnt get it

[@MJawadSial]

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

[@woohwison3296]

좋은 강의네요

[@kamyar9782]

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

[@mariaalyssalopez9884]

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

[@ernestovalverde2394]

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]

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]

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.

[@linhgabrielnguyen2952]

It is super clear and super easy to understand.

[@misafirkullanc4658]

Thanks so much i understand very well👍🏻

[@nyxfairy6538]

this is so difficult

[@dittyesq]

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]

Mental Abuse To Humans

[@ThatDudeEddiee0]

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]

No worries. Watch it again and again...

[@St-sz8oh]

Richard Smith no

[@beserned1347]

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

[@blkbaboon]

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]

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

[@beserned1347]

Minteew bruh thanks i was 12 when i did this

[@lemon-vy3mj]

:c

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

[@muhammadsharif6249]

You helped me alot thanks!

[@guys-xo1pw]

Can we get held back in online school?

[@tharushadakshaka166]

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

[@bareaahmalik238]

This video helped a lot. Thanks for saving humanity.

[@GodOfFools]

It's been 7years since this video was posted and I'm watching this a day before my test

[@KarlRuizS]

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

[@shawnputh9245]

Julio Ruiz r u dumb

[@everettwebster5524]

Change the speed of the video

[@mikey20is]

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

[@joannaathineosmathematics5706]

Sure! That happened to me too. He is amazing teacher

[@ammarkhalid8719]

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

[@drewabbott2016]

Thank you, sir... much appreciated.

[@shaundellsolomon4668]

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

[@ericaross5936]

yeah it would.

[@Michael-cc4qf]

ya he changed it after

[@ThatDudeEddiee0]

Lol he corrected it

[@subhadeep5924]

Watch the whole video before commenting.

[@joannaathineosmathematics5706]

Yap he corrected it

[@chwibii]

im crying because i cant seem to understand this💀

[@mahendrasubbu2644]

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

[@Allen-cx6yi]

if only all teachers teach like this

[@abutalhamahmud]

(y)

[@minerfreakpvp6954]

Doesn't this go towards programming?

[@minerfreakpvp6954]

Computer Programming*

[@cheesebandit6148]

@@minerfreakpvp6954 I think it can.

[@salmael-amin159]

Great lecture. Thankyou

[@walletadhd7701]

When your in a class for 2 months now, yet this guy teaches you more than your actual teacher did in 7 minutes.

[@shivshah525]

maths is very much cool thing !!!!

[@msp_gerodiasjhannrussel.j8216]

shiv shah stop it get some help

[@paigesaunders2531]

shiv shah ew

[@ahihi2002]

you need some Milk

[@aroomakhan7256]

the very best work and greatly help us.

[@moicaalim8596]

Thank You. I understand it

[@ratifiedratty101]

I still don’t get it 😑

[@6ra9]

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

[@6ra9]

oml staph.😂😂 yes i am jesus

[@ernestovalverde2394]

ImAnArmy kzbin.info/www/bejne/h2mugWBvotKtZ7M 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]

i understand it now

[@amrsalah4]

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

[@kepler4192]

My teacher teaches like you tbh (for the first time in history) he even sometimes removes lessons that aren't important at all or we already took it a million times (omg I'm so lucky)

[@Randomguy-rc1ei]

If my teacher taught me like this then i wouldve been a bright student.Here in India they only do the exercises and teach us how to do the exercises, they dont really concentrate on teaching the real meaning and concept behind anything

[@itzvoid4689]

what the heck

[@ramsinghbihola5429]

AJ jones t

[@ramsinghbihola5429]

AJ jones

[@azi9300]

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

[@wildrain8602]

Moonlight Hallow me too

[@DarthTwilight]

This makes perfect sense.

[@kashafanjum8706]

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

[@vbrr6508]

waste of time

[@sarahmoriyam8811]

no hater

[@Ruby--.]

This is actually understandable

[@genersonmaghari8470]

Im starting to get interested in this math thing

[@Leylayeesshh]

I am from azeribaijan.THank you very much teacherrrrr