Properties of Functions - Even vs Odd (Precalculus - College Algebra 8)

[@nehaljhirmaria]

Your biceps are an even function!

[@VieciTheengineerastronaut]

YOUU LITTLEEEEE .AAAAAAA.. 😂😂😂😂😂😂😂😂😂😂😂

[@mr.a9241]

Damn 😂

[@naylinn3402]

😅

[@wearegettingdumber...2263]

I'm in Calculus 1 and this has been by far the absolute best explanation of this concept I have ever seen. You are an awesome instructor, and I appreciate the content you are creating. Thank you so much!

[@mattdrafted2024]

I agreed

[@ClaytonLivsey]

Whenever I have problems in my life, I just remember the great advice Professor Leonard gives at 24:57

[@23Padron]

Attention everyone in the comment section. This is the best mathematical video you can watch. That is all.

[@aalekhrasal4246]

This is by far the best explanation of this concept. I FINALLY get it! Thank you so much Professor Leonard

[@philosophertiger4124]

This helped me better understand the difference between even and odd functions. Thankyou for this lesson; I am watching these videos alongside a Khan academy pre-calculus class in order to get ride of my math anxiety for trigonometry.

[@SH-cj5qu]

Your voice is so calming, i've learnt alot thank you

[@raiyanreza9764]

all that hand gestures helped me understane old functions finally!

[@mattdrafted2024]

You are the best Professor Leonard. Thank you for all your hard work.

[@D34DmAn]

Rest in peace, I’ll always miss your videos..

[@mridulkotriwala2265]

@ Professor Leonard I am from India... really thankful to you for your videos .....you made maths very interesting for me. You make concepts look so easy .....I can't say how much I thank you......you are a superhero... ❤️❤️Thank you

[@serafin8541]

When my brother was in high school he said that these concepts were very difficult for him to understand. I showed him this video and you should have seen the look on his face... thanks teacher.

[@harshivchhabra4180]

legit the best professor I've had. I will donate a shitton of money to you once I start earning.

[@gaganthegamex4184]

I trust you because you got bigger biceps then mine

[@georgesadler7830]

Professor Leonard, thank you for a beautiful explanation on the Properties of Functions that focus on Even and ODD functions. Even and Odd functions exist everywhere in science and engineering.

[@heydyvex]

You are so good at this, helped me to find beauty in math THANK YOU, I'm waiting for linear algebra

[@waryjelly]

Thank you so much for making these videos! I struggled with math my whole life! You helped me pass my college algebra class!

[@nancyspicer4337]

thanks I am glad I found your way of teaching it explains so much that I am now ready to take the test in math.

[@maximoleon5295]

a huge thank you to you dear teacher

[@kavitaarya9327]

Sir u are best teacher in u tube. U always take doubts of student which always make misconception about the topic. Thank u so much sir .

[@letlhogonolomotebe7663]

The best professor ever...

[@Saundaryassp]

Thank you so much.

[@theworldofcreativity9071]

I was going to ask if I could write -f(x)=f(-x) instead of f(x)=-f(-x) but you cleared my doubts at 14:56. Thanks so much prof. Leonard!

[@jos2294]

Please do Linear transformations and vector spaces

[@zakerhussainnazari4064]

Thank you , thank you , thank you..............................................................

[@HylianEvil]

Clicked because of the guns. I even learned something too!

[@Stone_r666]

😂 I feel you. The superman icon is too fitting.

[@mohammedelhassan2348]

Five years later, I clicked also to see the guns lol

[@ALEX-bk5qm]

THINKS U SO MUCH u helped me a lot i love the way u teach

[@socialonly4491]

Woooow , this explanation is powerful, thank you a lot I do appreciate it🙏

[@johnx5k]

OMG 😳 THANK YOU !!!!!!!! Soooooo easy… after I learned…. It make so much sense

[@XmonachosX]

Watch at 1080p guys . It's amazing that way

[@polouu4377]

you're amazing dude

[@shaniyadav3823]

I am your big fan

[@shaniyadav3823]

Your physic and teaching method

[@cs4maths610]

Explanation is super IAM also maths lecturer

[@aminmoafi5148]

Thanks, professor!

[@icee562]

This comes of great use in Fourier Analysis!!!

[@TheEndernal]

I’m going to try and take calculus in my freshman year of high school

[@karan_karan_karan]

at 12:25 my mind was blown... THANK YOU!!!

[@karan_karan_karan]

likeeeee it all clicked thank you!!!!

[@johnlouisville]

Great explanation of a confusing concept.

[@deepanjan.sengupta]

Hi Prof. Leonard. Could you create a KZbin payment account for your subscribers ( apart from Patreon)? That way it would be very easy for us to support in whatever we could. You are the best Math teacher on planet 🌎. Regards and Respect from India

[@fauzanputra3220]

Very good

[@Peter_1986]

lol the subtitles at 20:40. _"That's what God looks like"_

[@acer1748]

Not even taking calculus but enjoying watching!

[@ElNietoPR]

Still buff AF

[@rohitbosh4349]

I have a question.... Suppose f(odd)=g(odd) and f(even)≠g(even) Or, f(even)=g(even) but f(odd)≠g(odd) Then can i say f(x)≠g(x) [if x if integer] (Is this correct?)

[@HeyHey-np5gq]

ok man, whats is your bench, and do you do legs

[@ProfessorLeonard]

Love Leg Day!!

[@HeyHey-np5gq]

@@ProfessorLeonard lol good, in calculus 3, all the guys wanted to know was if you do legs. thank you for answering our biggest question in life

[@tiborkemeny8644]

@@ProfessorLeonard Then proof it :)

[@bernd8608]

Should I learn differential equations before or after taking calc 3? What about probability/linear algebra?

[@jamador408]

I learned it before calc 3. It wasnt bad at all just got to make sure you go over partial derivatives which isnt bad. Also, have your calculus techniques down! (Integration, differentiation)

[@zeeshan7372]

Mind blowing

[@muhammadahmedjaved7691]

You are a very nice teacher

[@captainjacksparrow933]

The example with a hyperbola defies the definition of function by vertical line test so how can we term it as odd function?(doubt)

[@shaniyadav3823]

Sir please tell me your diets

[@iyalodeolajubu6653]

true

[@alumi9818]

at 22:20 you wrote that = -3x^3 + 5 -> -(3x^3-5) shouldn't it be -(3x^3+5) ??

[@felliesweetie]

No! It is correct how he wrote it! -(3x^3+5) = -3x^3-5

[@paulmaggiar8274]

Sundae, you are correct. 5(-x)^0=-5. When you factor out the -1 you get 3x^3+5. This is an odd function

[@paulmaggiar8274]

@@felliesweetie 5(x)^0=5. 5(-x)^0=-5. Sundae is correct. This is indeed an odd function as can be verified on a graphing calculator.

[@manishpingale6558]

Legend!

[@TwentyThree-23]

At 6:25 Can I write the domain as the following: { x | -4 < x < 4 } (The signs would be greater than or equal to, I just don’t have the symbol. And in interval notation [ -4 , 4 ] ? Also would Range be written as { x | 0 < y < 3 } again, the signs being greater than or equal to.

[@cookhindigaming4795]

Yes Dude it's perfectly fine

[@hkanhai5094]

Hi professor good afternoon. Are u doing any different course in class where u can Video it as u did for your calculus videos ?

[@redetmillion1338]

you're total genus's

[@onlineskillsbyimranbilal]

Verybhelpful

[@Euphemia-em8fe]

day 2

[@nishagc9753]

Could you give the lecture of probability!!!!!!

[@mahmoudelssawy245]

He already did.

[@Clutcch]

8

[@anupammishra2719]

Thank u sir😊😄💪.Here is something sweet for u🍨🍧🍧🍧

[@aaqibali9349]

Prof. plz make videos on Spatial functions . Like bessel .legendre functions etc

[@mattdrafted2024]

You are a total Idiot

[@mustafamalik4211]

When you are browsing through differential equations and you bump into the precal series. Good time.

[@omarel-shetehy2665]

16:41

[@isobar5857]

Bit confused sir, at 12.22 the top right graph will give the same output for -4 and +4, i.e. zero. Isn't that the definition of an even function, not an odd one ?

[@alex-ie8tp]

the definition should be valid for every point, not just one

[@JLiptak]

Actually I've never seen algebraic expression of odd function as you wrote first before, thus f(x)=-f(-x). But I have to tell you that I like it better than traditional notation f(-x)=-f(x). In the first way, I would say that it's more obvious for students to comprehend what exactly this algebraic expression means. :)

[@jeanjulmis2347]

it depends on how you wrote it. If you isolate f(-x) by multiplying by negative 1, you will get: -f(-x)=f(x)=> f(-x)= -f(x).

[@pkus]

​@@jeanjulmis2347 he says f(x) = -f(-x) according to his graph, f(1) = 2 and then f(-1) = -2 but -f(-x) gives me -(-2) = 2? right?

[@jeanjulmis2347]

@@pkus right on!

[@2pacgilsi589]

Easy ❤🎉😊

[@souzou1000]

where are the rest of the videos?

[@godstroke]

professor "how are you supposed to count your sets if you can't math?" leonard

[@sscc587]

Dammmmnnnnnn!!!!!

[@jondwyer9323]

Lol Lenny getting a pump before recording?😎

[@taz7275]

Couldn’t pay attention

[@mahalingama4162]

What KZbin channel which are helpful for engineering 1st year mathematics ? Anyone suggest pls ?

[@mahalingama4162]

@Oscar Rivers what ? U mean this channel ?

[@mahalingama4162]

Can anybody tell does this channel contain functions of several variable !

[@krystinasaragos1535]

I just don’t understand. Is precalculus just intermediate algebra with trigonometry? Cause didn’t we learn this in algebra class?

[@ProfessorLeonard]

It is VERY similar, but Precalculus will go much more indepth in just a bit

[@krystinasaragos1535]

Professor Leonard ... So at what number video do you start teaching precalculus? I swear all of the videos I’ve watched so far, currently on this one, are exactly what I learned in my intermediate algebra class. So when does the precalculus start? Am I still not getting it? 😂

[@TheMountainBeyondTheWoods]

Krystina, for those of us that haven't been in school for a looong time or I never even learned it while in school this is extremely helpful. If you already know this part why not just skip ahead to a video where the Prof is teaching what you need help on?

[@felliesweetie]

@@krystinasaragos1535 Patience!

[@TheEndernal]

I’m an 8th grader who binge watches khan academy so I’ve learned these concepts but it’s good to get another explanation. This channel explains well

[@hz6612]

thank you mr leonard , i will pray god to bless you and pray god to make you muslim

[@Antri-jd9jy]

Was necessary the last part? We are here to learn, keep your religion to yourself.

[@hz6612]

@@Antri-jd9jy the greatest knowledge is knowing that god is real and islam is the true religion

[@Antri-jd9jy]

@@hz6612 Good for you but keep that to yourself, just as I respect you practicing your faith, also respect other non Muslim people.

[@hz6612]

@@Antri-jd9jy i say i want , you just want and what im saying god wants it to be said as man have a task of informing about islam , but people like you i think they dont want anything about religion to be spoken , if you dont like it then just ignore me but thats not of your buisness if me or any other person wants to speak abotu islam , because we want think about what you like and waht you dont before we speak about religion , cuz some people like you would find it a nonsense but many other wouuld find it very helpful. and now learn how to deal with it .

[@Antri-jd9jy]

@@hz6612 Would you kill a non Muslim? Genuinely asking.

[@eatinsomtin9984]

All the woman in the comment section: 👀

[@idealisticusgenius8089]

Первый русский

[@ryleeleavitt8522]

What does this mean