Recognizing odd and even functions | Functions and their graphs | Algebra II | Khan Academy

[@lisa5hot]

you explain so beautifully you make me want to cry Khan. You a true homie

[@lisa5hot]

Zorro Yes, Zorro, it is my profile picture

[@jamalimam3784]

Let it out son

[@danielross5931]

lol

[@hassantakruri9702]

His name is sal lol, khan academy is the name of the institution.

[@Anish-IITP]

@@hassantakruri9702 yeah only muslims and south asian would find it soon 😂😂

[@jaymodi5378]

my actual math teacher hasnt even shown up to class and expected us to learn this. Now i understand after watching this video. Thanks G

[@sashaboichuk8565]

literally the only thing i say in school when i dont get something. "whatever ill just khanacademy it later". it's become a verb for me and my classmates

[@ademolaashaye1632]

You are just simply good. I wish Professors would be forced to watch Khanacademy just to really learn the art of knowledge transfer.

[@MrTomdabomb1313]

Every time I watch these I admire your mouse control. I would never be able to write words so neatly with a mouse.. Also, your concept explanation is impeccable - the way you introduce new concepts is very understandable and easy to comprehend, I just wish i didn't leave all my study to the last minute so I could watch all your videos!

[@nvsreddy]

He uses a tablet and a stylus not a mouse.

[@pacpep5086]

nigg@ you been replying to a comment that is 9 year old@@nvsreddy

[@yuvrajbro8882]

What a simple explanation ...... Indian Teachers need to learn from him.

[@bp56789]

I think the "odd" and "even" naming convention is due to the powers. x^2, 2 is even hence it is an even function. x^3 is odd therefore it's an odd function. This is due to the way negatives cancel: an even number of negatives multiplied become positive, and an odd amount of negatives multiplied is negative.

[@xXxTuN3RxXx]

@khanacademy your an absolute hero when it comes to solving my math problems, I really appreciate all the effort you put into your videos, thanks a ton.

[@TuscancowOfficial]

Learned this in class, but found it hard to comprehend the notes my professor gave us, and textbook is rather all over the place and breezes over this. You made this so easy for me to understand. Thank you so much!

[@williamhorn411]

Perhaps the reason why they are given the name "even" and "odd" functions has to do with the "evenness" or "oddness" of the powers of x in the function? For example, x to any even power will invert the original sign of x, whereas x to any odd power will keep the original sign of x. Therefore, any function with all even powers should be considered even because we know from this rule that it will satisfy f(x) = f(-x) (since all signs are inverted). Likewise, if all powers of x are not even, you know you will have at least one different number because one of the x's will have a different sign, therefore not satisfying f(x) = f(-x) but rather satisfying f(x) = -f(-x) (so called "odd" functions, when a power of x is odd). However, I feel like I'm missing something for functions are are considered neither even or odd... I'm just a student trying to make sense of this, if anyone wants to jump in and correct this or verify this, I'd appreciate it.

[@sagynzhanabduakhap7542]

you are correct about the powers--function with only odd powers will be odd, same with even! functions that are neither even nor odd will include both even and odd variables. That way one variable will change, the other stay the same when plugging in -x, and the y value will be completely different--not the exact value as it was nor an exact negative, just different. For example, 2x-x^2 if we plug -x then it'll be -2x-x^2. did not remain the same nor did it become a negative version of the original function. and if you graph it, it will be a parabola that was shifted from the y-axis, therefore it's no longer symmetrical around the y-axis

[@hitdoctor24]

Can't wait for the day where my life will depend on whether or not I can determine whether a function is odd or even. Thrilling stuff.

[@totasalam7060]

best teacher ever..thank you so much

[@scoutinfashion]

Thanks so much Khan! This video made more sense to me in three minutes than my teacher did in an hour!!

[@NicksDomain101]

You draw better with a mouse then I can with my hand haha

[@lisa5hot]

he probably has a pad he writes on

[@knowledgepower7286]

frida aleksey I've seen a vid of him on the news, he uses an electronic pen & a pad, like you suggested. Very talented dude in many subjects... makes me wish I put more focus on education when I was in High school but then again my dad wasn't a Doctor like his and I didn't go to MIT or Harvard like him... all I can do is focus on NOW & learn everything I can...

[@waads19]

NicksDomain101 SAME

[@dalenassar9152]

The best examples of even and odd functions are COS(x) and SIN(x) respectively. You did get a COS-like wave in there, but never called it 'COS'. Thanks for the best videos!

[@bradenlheureux8509]

Thanks, I was looking at my math book and my brain turned to mush until I saw this.

[@Mpthedawn]

great job broo....used ur vid for my signals & systems class keep it up dude

[@michaelmurdoch]

Awesome explanation. Thank you!

[@mohamedfarah3844]

great video .... thank you dude

[@2nconway]

Great lecture, I wish my Professor was as proficient in his lectures. Thanks!

[@ryanschott7732]

Really helped out with my quiz and homework thank you

[@irreplacebleluv]

My teacher should just let us watch khanacdemy on our smartphones it would save everyone timee!

[@newqulipseova49]

Very nice explanation

[@EpicRoLLerCoaSter613]

4:25- angry chinese guy

[@wadehosking4446]

Lol, nice.

[@hamzahyamin2689]

😂😂😂😂😂

[@malaikapatro7835]

😂

[@architchawla6278]

Thanks! best math class ever!

[@ZealousAnubis]

I have to teach this concept tomorrow; I'm so nervous...

[@hasansaleem4983]

@@DidoFido7 you are asking this question after 8 year?!

[@emmaevans9249]

@@hasansaleem4983 yes

[@CODmaster3171]

You sir are the reason I pass classes

[@Reklemer3]

Gold, thank you.

[@thestig560]

I literally spent all day trying to figure what this all means. Wish I would have stumbled onto your video 12 hours ago

[@xirsiyarre1630]

You help me alot

[@MassEffectReaper]

Thanks Khan, you're the man!

[@ajskilton]

Brilliant as usual, thank you.

[@petemitchell1403]

thank you very much,always appreciated your unparalleled teaching

[@mahjoubahmed1287]

Thank you so match good explain

[@ALMshtFSaliH]

thanks man u do to me a great thing

[@ashleypizana1114]

Thank you! This helped me a lot!

[@niceguy4801]

Thank you sir!

[@xirsiyarre1630]

Thank you teacher

[@gonnendaube7512]

I think it is called "Even Function" because every function that it's power is even , like x^2=f(x), or f(x)= x^4+x^2

[@Lolzwutz1]

Yes, but the f(-x)=f(x) solution is very useful for when the equations get quirky later on

[@arifzakaria4832]

cosx is also an even function

[@KrisPBacon69]

12:23 it sounded like he was gonna say more things, but the video was cut

[@anthonyferretti737]

Business major here. Thanks!

[@PandaGirl116]

Thank you!

[@soikatmaji4685]

Thanks for the awesome explanation :)

[@boogychan]

6:49 that is exactly what I thought...😳😄 'reflect and then take negative'

[@LaurenOrder16]

he has a good voice.

[@jazzymintz]

Thank you! I have a midterm tomorrow... hahaha....

[@paulceltics]

thanks a lot

[@duran9987]

no, if its odd its symmetric across the origin not "both axis"

[@transAmos654123]

God! You explained way more clearly than my teacher.

[@toobakham8770]

Dude you're cool How do you manage to teach every subject perfectly.

[@gulnaroguz2510]

by learning perfectly what he preaches before he preaches

[@ImSzzaass]

great video, but i think the most common Odd function would actually be f(x) = x

[@cassied9327]

This helped so much 😭

[@ErickVazquez16]

Which app are you using? Really a good math video.

[@kikbxr94]

there is a link between even numbers and even functions, i just checked in my University Calculus text, and it says that if x has a power of an even integer, then its an even function. Same thing for odd functions. Ty anyways for help :)

[@justtimepass7838]

Nice explain

[@alexv2401]

You just solve it algebraically; plug in "-x" into the equation. After plugging in "-x" into the equation, if the same exact equation is returned, such as in f(x) = x^2, then the equation is even. Otherwise, if the equation that is returned is the original * -1, then it is odd. For instance, f(x) = x would be an odd function.

[@Anish-IITP]

Is the second even graph is a graph of slope of a graph having sharp edges?

[@MSULightWeight]

Great video

[@zoenoelcruz2682]

an odd function is when the graph is reflected on the ORIGIN where -f(-x) = f(x)

[@anwerosama94]

Hey thanks mate :)

[@josephjithu8484]

Amazing buddy

[@menaahjuma]

Thanxxx ... ur so amazing

[@livfrazier6295]

Same here. I feel ya

[@factsamaze6656]

Can a function be both even and odd function at the same time?

[@ghostboyindisguise]

The relationship between odd and even function are the exponents.... and x^2 is more likely even and x^19 is most likely to be odd

[@motoxracer989]

how do you figure out if its an off function when all your given is a table with values, without graphing the table?

[@MsViviVP]

Doesn't the exponent (even or odd) relates to determining if the function is even or odd?

[@zaintalat8607]

Love u bro

[@sophiarodriguez1861]

You're saying the "even" doesn't necessarily means "even degree", but "The Organic Chemistry Tutor" says that even means even degree. Which of you is right??

[@barrydavis331]

Every exponent needs to be even.

[@bulasinha2772]

the organic chemistry teacher is right. but sal corrected the mistake in his next video :)

[@neonskie7008]

Oraganic chemistry is right

[@kunalrawat5472]

Can you also say in the graph (s) of odd functions the shape from 1st quadrant would have a rotation of 180 degrees about the origin? Because the shape of f (x) = x^3 in 3rd quadrant is same as if you rotate 1st quadrant's shape through 180 degrees about the origin

[@realjatt10]

Sal, you're a god

[@piscesgirlfriend]

this is so helpful, especially when your teacher can’t teach and you have a test tomorrow lmao

[@supergeebaby]

how can you tell if its a odd or even or neither by just looking at the function rather than drawing it out every time?

[@Maui-Lily]

Just to make sure I'm understanding this, y= F(x), and when doing even-odd properties we are always reflecting over the y-axis?

[@mrpleasurehead]

Hi. In the video, you say you can't see any correlation between Even + Odd functions and Even/odd numbers. But, while watching this it became evident to me that Odd powers contribute to odd functions and Even powers to Even functions. Could this be the case?

[@alyssaphilip2404]

very good vid yayay

[@musicx24]

(x^2+sin^2y)^1/2 root(x square +sin square y) is even or odd function

[@nasiryounis8202]

Amazing

[@norahsradan812]

For odd functions, does it always have to start from the first quadrant?

[@عفافالحواتمه]

Hello Thanks a lot Can I know what is the program you used in the video to explain even and odd functions?

[@Tiippyyy]

@motoxracer989 You plugin the given values into the function.

[@abroobatool1626]

a function f(t) =2piet-t^2 is even or odd??

[@zainulabideen7210]

sum of cos cube x and sin square x will always be odd or even plz reply

[@danieldamaskinos]

Even

[@hamzazafar-laststand7115]

Very helpinggggggggggggggggggggggggggggggggggg

[@harshitaapandey1402]

In 2:59, you said that there is no correlation between even numbers and even functions, but actually even functions are always x^2,X^4,x^6... the power is an even number

[@realFriedrichHayek]

yes u r rgt

[@amerkanj5475]

He just used those as examples. But as he stated, a function is even if f(x)= f(-x). So if we do (2)^2 and (-2)^2 they both give us an answer of 4, if we do (5)^2 and (-5)^2 they both give us 25. So there is no correlation between even numbers and even functions.

[@Unataka101]

for it to be even it has to be symmetric only to the y axis, not the x or origin or x=2????

[@JoshuaDavidBrown-Jaded423]

Um, am I being over simplistic, or do all even functions only have even exponents(x^2, x^4+x^2), and odd functions have only odd exponents(x, x^3, x^5-x^3), while combinations of odd and even or the addition of numbers makes them neither odd nor even?(x^4-x^3, x^2+4)

[@jookie4207]

Man, my math teacher could’ve explained this so much better lol

[@----700]

If x(t) is even then why x(t -1) is not even? Please do explain. I will be highly thankful.

[@maryjoseph3303]

in the second example of odd function he drew, there are two values for f(0) ..so it's not even a function,right?

[@aussiefruitbat]

how we can know if the 2X/X^2-4 is odd or even function

[@ayeeitsalex2232]

you're so awesome =D

[@matthewcoleman9780]

Mr Woods class wya?

[@Whitsoxrule1]

The second even function you drew looks like an angry face XD

[@St0bie]

I remember even and odd because even functions are even degrees, odd function are odd degrees

[@Jakenbake98]

is that 100% true all of the time? that would be a really easy way to remember

[@St0bie]

Ya, but not all functions with odd degrees are odd function (same is true for even). In order for a function to be even, every exponent in the polynomial must be even. The same is true for odd. If there is a mixture of even and odd exponents, its neither. Hats easiest way to tell because graphing it takes forever

[@Jakenbake98]

okay thanks

[@thecs13yea]

In pre calc from now on imma be like whatever's I don't need to pay attention, I'll just 'khan' it later ;)

[@cybertools8560]

4:23 its a frowny face.

[@fhggcg6221]

Min jey min madrest el sade2🧐

[@hkgames4528]

Ane😅

[@fhggcg6221]

@@hkgames4528 😹😹😹😹

[@BONIFASI007]

how can u tell without graphing?

[@thesocialgod]

Isn't the last part of the video missing???