Determining if a function is even, odd or neither (KristaKingMath)

[@LittleVampers]

This 4 minute lesson literally just covered what we were going to do tomorrow for pre-calc in one hour. Lessons like these are quick and understandable, which is a must if you want to get ahead on homework (especially if you have marching band and don't come home until 9 or later).Thank you!

[@kristakingmath]

+LittleVampers That's so awesome that you're prepping ahead of time! Glad it could help!

[@pepperrgirl]

LittleVampers 😂😂💆This chick is my girl!! Thanks for the video, you have a gift. Mine spent 1/2 hr drawing/writing a lot of stuff/muttering to himself/erasing stuff. Finally I can finish my homework!! Will have refer back to my notes to see why this fool turned this 4 min explanation into a War and Peace tome. Thank god I found you on my second day of class.

[@kristakingmath]

YES! Second day of class.... that's awesome! No epic math sagas here, just keepin in simple. :) Can't wait to help with the rest of the semester! :)

[@landryjames95]

THIS IS PRECALC??? We’re doing this in algebra 2 right now

[@torlarsen2212]

Annie Bee I feel ya Marching Band is sacrifice one must make

[@21xy10]

slept in class for 45 min, woke up confuse. watched a 4:22 min video......magic

[@chennanzanxuan828]

LOL got the same feeling

[@strollas]

lmao except my teacher literally didnt teach

[@cloutfisher7714]

School in a nutshell

[@lizbethsanchez7853]

You taught me in minutes what my teacher could not teach me in hours. You're awesome

[@kristakingmath]

Aw thanks! I'm so glad I could help!

[@liz1355555]

Because of you videos I finally understand things that I can't pick up from my professor who I take class with 3 hours a night Mon-Thurs.Every time I learn something new from your videos I don't know whether to cry or laugh or scream or what...so many emotions run through me all at once..God bless you dear child..God bless you..

[@kristakingmath]

lol...I'm so glad I can help! :D

[@thiendo6647]

I have a Calculus test tmr and this video saved my life. Thank you!

[@kristakingmath]

Thanks! Yes, I'm hoping to add Fourier Series. I know there's not a ton of material out there right now. I'll try to get some up as soon as I can! :)

[@DogeFrom2014]

Wow this 4 minute video helped me way more than what I learned in class!!

[@kristakingmath]

+DOGE™ Nice!

[@awonderfulfeeling8588]

DOGE™ Lmao I love your profile pic, it's always hilarious when dogs give you that silly glare out of the corner of their eye 😂😂😂

[@MaritimeLobster227]

I just started first year calculus at university and your videos are helping me through a lot of the things i didn't understand in the lectures, so I just wanted to say thanks alot.

[@alygirl011]

Not going to lie, your videos are more helpful then my college professor... lol Thanks!!!

[@kristakingmath]

LOL, well I'm just glad they're helping!!

[@guidofeliz8384]

What's amazing is the fact that she does not have a math degree.

[@dmitriymelnikov7301]

What’s fucked is I gotta do this in junior year of high school, Literally on the 2nd week of school

[@crocopie]

Hi. It would be helpful if you could show graphs of an odd, even, and neither function. Thanks.

[@lagunapiano3893]

Dmitriy Melnikov me rn

[@kristakingmath]

i'm glad you liked it! :) i have some functions stuff at the beginning of my calc 1 playlist, but i don't have much yet on imaginary numbers.

[@we.visuals]

Please become my teacher, you were able to simplify what my college professor taught in a 2 hour lecture! Thank you so much!

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@kristakingmath]

same thing... you'd plug -x in for x and then simplify. |-x| will always be positive in the same way that |x| will always be positive, so they'll end up being the same. which means that in the case of your example, you'll end up with an even function. hope that helps! :)

[@mattfox9919]

Your way better than my math teacher for sure

[@Grassmpl]

That's cuz your teacher does not teach post secondary. The professors there know topology, optimization, algebraic geometry, representation theory, etc.

[@kristakingmath]

because (-x)^4 must be calculated before you distribute the negative sign. (-x)^4 is x^4. only then can you apply the negative sign outside the parentheses, and you end up with 1-x^4. hope that helps! :D

[@kristakingmath]

I'm so glad the videos are helping! Good luck with calculus this year! :D

[@sudarshanroxx]

❤️❤️❤️❤️Love From India❤️❤️❤️

[@pietrom2]

Great explanation. The key, as you so capably presented, is to multiply the function by -1. If you return to the original function, it is even. If you return to the original function except with a -1 factored out, it is an odd and if neither of these two results occur, it's just that. Thank you very much.

[@sefaa4089]

THANKS SO MUCH YOU EXPLAINED BETTER IN 2 MINS THAN MY TEACHER COULD IN 1 HOUR

[@kristakingmath]

I'm glad I could help!

[@CloudMcFoxx]

The world deserves more teacher like you! Great job and thank you!

[@kristakingmath]

Awww, thank you so much, I'm honored!! :D

[@CloudMcFoxx]

Please excuse my bad spelling in that last comment, I typed fast because I was so happy to finally understand that concept! Then again you're a math teacher so you wouldn't mind haha. Anyway, you couldn't have made it any clearer, again thank you so much!

[@UnfoundMusic]

Thank you very much for this thorough explanation! I haven't seen anyone else make it more clear and you did a great job at helping me figure this out. Keep up the great work! :)

[@kristakingmath]

Thank you! :D

[@kristakingmath]

Wow, that's so nice of you to say! Glad you liked it! :D

[@mohammadahmedragab837]

this is the second video to watch on your channel, your style of teaching is concise and amazing 😃

[@Magpie5yndrome]

This is SO much easier to understand than listening to a Ukrainian professor who doesn't understand your questions half the time.

[@Grassmpl]

Pardon wu-at is it ze gu-es-chin? No un-zere-stand so-lee. Just mocking and faking an European accent here.

[@sashag2615]

You never fail to explain things in the clearest way possible, thank you! This channel has helped me so much :)

[@kristakingmath]

I'm honored! And I'm so glad it's helped! :)

[@ncalle8018]

omg you're amazing. I'm gonna ace this final now! my professor made it look so difficult but this is so easy! thank you so so much!! :)

[@j.simond6335]

Thank you so much. I am taking a pre-calculus class and the way the book explained this was overly complicated and I didn't understand. You are a god send!

[@kristakingmath]

So glad it could help Jennifer! 😀

[@MahmodoVX]

you are 3 in 1: intelligent , funny & pretty that's why we love you. if i pass my calc1 class , gonna give u special gift

[@Grassmpl]

You were in Calc 1 yet had trouble with some concept that should be clear no later than grade 11?

[@kristakingmath]

Great question! Even functions are symmetric about the y-axis, whereas odd functions are symmetric about the origin. If the function is neither even nor odd, then it won't reflect either of these kinds of symmetry. Hope that makes sense! :)

[@jaymackyt2416]

You helped me past my final. Thankx

[@kristakingmath]

jayveous mckinnis I'm so glad it helped, and congrats on your final!!

[@bendanoue6685]

I can't believe how easy this was. Thank you so much for making this video.

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@yurMommaSoFat]

hi I'm learning calculus, and my question is why do we care that a function is even, odd, or neither?

[@SwissExperiments]

+l la it could be useful while integrating. also for Fourier transformation. google it up to know more ;)

[@kristakingmath]

even functions are symmetrical about the y-axis, like y=x^2. odd functions are symmetrical about the origin, like y=x^3. if you're looking at a picture of a function that is not symmetrical about the y-axis or the origin, than you know that the function is neither even nor odd. :)

[@ThePerfect1077]

Thanks, that was crystal clear and straight to the point ^^

[@kristakingmath]

Thanks!

[@brennahamson6421]

This is amazing! I love my professor, but she taught this a different way I could not quite comprehend for whatever reason! You just saved me for my test Thursday!!!!

[@kristakingmath]

I'm so glad it was helpful, Brenna! I hope your test went great! :D

[@heshamalmalki8156]

ur the best teacher in the world

[@Grassmpl]

In lower division I agree. When upper division (3rd year or higher) math arises I'm your goto guy.

[@kennethhowell5291]

Thank you! Your online math courses are the best!

[@marathonpro92]

keep replaying the first second of the video without laughing hahahaha "(high pitch) Hi everyone!!"

[@joel1544]

fail troll is fail

[@Eddy2s]

Can't believe how easy this was, my teacher makes pre-cal seems a lot harder. Thanks for your help!

[@Grassmpl]

It's really not hard. Even easier than riding a bicycle.

[@PokegurlMisty]

i am crying thank u for saving me

[@kristakingmath]

i think they're trying to get you to realize that the function will eventually turn into something with an x^4 term in it, which means that it will have symmetry about the y-axis and be even. you wouldn't even have to deal with the substitution.

[@Bostonaustin25]

My teacher should not be qualified to teach haha this was so much better explained

[@Snacts]

you're very helpful, and I'm happy to see you still reply back to people even on your old videos! You are awesome.

[@kristakingmath]

:D

[@shadowravenbk7116]

Such a helpful video thanx!!! My teacher could never explain it in the way that you did! >.

[@kristakingmath]

+ShadowRaven BK You're welcome, I'm happy to help!

[@mor3569]

the last one comes out to be and odd function, f(-x)= -2x- (-x)^2= -2x+x^2. then when you factor out a (-) it gives you - (2x-x^2) which is your original function.

[@aboodmnasr]

why (-x)^5 stay -x^5 but (-x)^4 changed to x^4

[@kristakingmath]

because every two negative signs cancel and become positive. with (-x)^4, you have four negative signs, so two cancel, then the other two cancel. but with (-x)^5, you have five negative signs, so you can get two to cancel, then two more, but you've got one negative sign left over, so the answer is negative.

[@aboodmnasr]

Thank you that information hleped me a lot

[@laithshamlawi2754]

after hours of reading the book and watching videos with indian accents, i found this! simple and fast! thank you!

[@kristakingmath]

+Laith Shamlawi Glad you liked it!

[@vivianarosales1172]

doesn't a negative times a negative equal a positive??

[@quill6408]

+Viviana Rosales Yes, but a negative to any odd power makes a negative. it's just like -5 (-4) -1 = -20. The same applies to x... -x/\3 = (-x)-x(-x) = -x/\3

[@icronicfails2497]

If the power is odd its gonna stay negative

[@ellismitcheson9982]

help please... i cant see any odd power?

[@vaibhavsingh5894]

Really can't find better content than this .... you're great ma'am 😀...you are not getting better with time ...you started as better and now you're best😀🎉🎉🎉🎉🎉🎉

[@kristakingmath]

Thank you so much, vaibhav! I really appreciate that! 😀

[@traveler8010]

explains better than my teacher!

[@kristakingmath]

thank you so much!

[@traveler8010]

C:

[@kristakingmath]

Hi! No, you need to deal with the (-x)^4 first. Remember that you could write that as (-x)(-x)(-x)(-x). The four negative signs cancel, so you get x^4. But then you still have to apply the negative sign outside the parentheses, so you get 1-x^4. Hope that helps! :D

[@bencarllson1475]

Thanks! this helped so much!

[@jaydagreen1775]

everyone here is in calculus, but i have to do this for an algebra class i had to do on top of my current math class. the textbook i'm using is just dead weight, so thank you for this more in-depth explanation.

[@kristakingmath]

No problem, Jayda, I'm so glad it helped! :)

[@bigjayfitness]

thank you you majestic wonder of the world

[@LifeWithYourMum]

I'm going to go ahead and just say what everyone here is thinking. I wish you were my professor! You explained it so well that in a matter of 4 minutes I understood how to now solve these problems. I thank you, thank you, thank you!

[@kristakingmath]

+Michael Nunez You're so welcome! I'm glad I can help!

[@anoirtrabelsi8645]

You can be a partner with Khan academy !!

[@kristakingmath]

That would definitely be cool! :)

[@raj.k.kashyap]

Great Job! Keep it up! You made a simple process look simple, unlike many explanations which over complicate math often!

[@kristakingmath]

Thank you very much!

[@rjlast2655]

Pretty and Smart. A rare combo in girls these days.

[@jjramirez1125]

I'm taking an online pre-cal course. That means there is very little student/ teacher interaction. Your video has helped a lot. Thank you.

[@coltonpicazo2922]

um cant really concentrate over how pretty she is.

[@samuelfauteux6735]

From the second she said hi everyone, I really wanted to learn! What a lovely and intelligent lady! :)

[@ourfutureisdark]

your awesome thanks! i guess im gonna pass my pre-calculus final

[@kristakingmath]

I hope you rock it! :)

[@kristakingmath]

i think that homework problem was telling you that you couldn't use your calculator to graph the function, because you can tell if it's even/odd/neither just by looking at the graph. i think they were trying to get you to do it like i did in this video, where you actually prove algebraically that it's even/odd/neither. :) so glad it helped!! :D

[@stephenprice3357]

your voice scared me at the very beginning

[@SmokinLoken]

+Stephen Price I like playing the first 2 seconds of this video over and over. Makes me laugh every time.

[@stephenprice3357]

kmsl ikr i do too

[@cr07forever93]

+Stephen Price what is kmsl?

[@stephenprice3357]

malik zain killing myself laughing

[@cr07forever93]

+Stephen Price thanks

[@peterdefelice2698]

This one video has been more helpful then a week of teaching from my math teacher

[@xfeedmonster]

anyone come for the teacher and not the lesson?

[@leninistlemon6675]

**disappointment in humanity increases**

[@jamesretreat]

and then the ask "why the F"

[@yw900]

just human nature bro

[@ronronn3148]

LOL

[@awonderfulfeeling8588]

I think you meant to say something more along the lines of... "Anyone come for the lesson but stay for the teacher?"

[@luzdc9]

I wish I have found this videos when I was in college and not after.. I finally understood how to prove if it is even or odd.. Thank you so much..

[@kristakingmath]

Luz Batista You're welcome, I'm so glad it finally makes sense!

[@farhaannishtar786]

Luz Batista wait then what are you doing here X,D

[@felixlokz]

I find it joyful watching your videos

[@livelovejacky]

thank you for this! I have a math test tomorrow for my pre calc class and I'm only in high school but my teacher already is terrible. Thank you so much!

[@austingage6465]

My instructor is absolutely horrid when it comes to teaching. Thank God for you, your videos are amazing!

[@kristakingmath]

Aw thanks! I'm glad they're helping!

[@dlocks0000]

I was trying to figure this out for days and you made it seen so incredibly easy. Thanks so much for this video,you explain everything very clearly.

[@kristakingmath]

I'm so glad it helped and that's it's more clear now! :D

[@elizabethkaur7095]

Probably one of the best math help videos I've ever used!

[@BokChoyLee]

This video is short and straight to the point! Clarified everything for me... Thanks so much!

[@kristakingmath]

+Mat The Filmer Awesome! Thanks for the feedback!

[@BevDahBest]

Wow, i finally understand this! You're much better at explaining than my teacher, who just assumes that we understand it! Thank you!

[@chiviza]

Awesome! so simple, yet my professor never explained to us how to do this and assigned us problems that require us to do this so i was kind of lost. Thanks!

[@kristakingmath]

I'm so glad it helped!!

[@kristakingmath]

you do the same thing i did in this video. if you plug -x into f(x)=tan(x), you get f(-x)=tan(-x). you can't simplify that to -f(x) or back to f(x), so f(x)=tan(x) is neither even nor odd. :)

[@jeniferchowdhury8073]

I'm the only junior in my honors calculus class and you help me so much explaining it in details. Thank you so much :)

[@kristakingmath]

+Jenifer Chowdhury You're welcome, I'm glad it helped! And good for you, I hope you're doing great in your class!

[@marleeyork7728]

This is exactly what I needed for my test tomorrow!!! Thank you so much!

[@kristakingmath]

Good luck! I hope you crush your test! :D

[@envy-my-wishes2398]

finally!!! someone that knows how to show and solve a problem!!!!

[@dasoyee]

The video helped so much! Thanks for posting this! The great quality of the mic and steady work with the chalkboard were a giant plus! Great video overall!

[@dennisvijverbergbrakesrele6098]

Excellent explanation! Thank you very much. In a couple minutes you made understood what my professor doesn't in a whole class.

[@youtubetest3770]

Very clear and methodical, and the writing is calligraphic: bravo!

[@kristakingmath]

Thank you very much!

[@Perrytheplatypus11]

Stellar video that explained the concept to me in a matter minutes, turning a once difficult topic into an easily understood one.

[@kristakingmath]

Elias Taveras Awesome!

[@gaWalt]

Very good explanation of even, odd, and neither functions! Thanks for your help.

[@kristakingmath]

eGliderman You're welcome!

[@julienelson6506]

Thank you. You explained it much better than my professor and with a much easier explanation. It is so simple they way you explained it!

[@eduardoguadarrama9860]

OMG THANKYOU SO MUCH😀😀 . I started pre-calculus and my teacher just started school the second day but giving us work to what we didn't know.

[@kristakingmath]

You are so welcome! I'm glad I can help along the way. :)

[@KairiCatVideos]

it seems like everything before video 30 in the playlist was pre calc for me but I dont remember ever going over this so here I am. These videos are a god send though. passing calculus here i come

[@kristakingmath]

You're going to do great! :D

[@hectorgonzalez6341]

This helped so much, I have a test tomorrow and I had no idea what this was until I saw this video. Thank you, you've helped my grade.

[@jessebeso8143]

Wow! my college professor was not able to do that, or the math lab and in 4 min I learned from you. Thank you soooooo much.

[@kristakingmath]

you're welcome! i'm so glad it helped!

[@mareasoceano5566]

You're a better teacher in 30 seconds than my math teacher in one month.

[@kristakingmath]

+Mareas Océano I'm happy to help!

[@johnharms4779]

Oh, wow. Another KZbin tutor that challenges the credibility of my college professor. Gotta love it!

[@jetswhiteout961]

This was so clear, was confusing in my calc lab but this saved me for my quiz tomorrow. Subbed!

[@dangchanneldeg6948]

Oops! Where was this when I took my quiz, I have a College Algebra final tomorrow. I'm coming back to this video before I go to bed tonight. Thanks!

[@kristakingmath]

Daniel Gurule You're welcome, and good luck on your final tomorrow, I hope it goes great!!

[@polocisneros]

Oh my gosh Krista! Thank you so much for this explanation! I've been trying to grasp this concept for the past 2 days reading my Algebra text book with no luck, too much detail! & I just happened upon your video thank God you came through crystal clear! Thank you (-oo,oo)

[@kristakingmath]

You're welcome! :D I'm so glad this helped clear things up!! :D

[@OverBanned]

Thank you very much! Super useful. It made look super simple, and easy to understand. Have to admit that even made me feel stupid for not understanding in class, but I guess it's the way that my professor explained it. Once again, thank you so so much, I am sure that I will now pass tomorrow's exam!

[@kristakingmath]

I'm so glad it helped, and I hope the exam went great!! :)

[@nouraalmarri8116]

thank you so much this saved me !! i spent two hours trying to understand it on my own and your video cleared it up for me in four minutes !!

[@kristakingmath]

Oh good! I'm so glad this helped clarify everything! :)

[@noelrisco5057]

Thank you!!! I was absent that class, but now I don't even need to ask the teacher!!!

[@effemmeli]

Cramming for my Midterm right now. Helped a lot thanks!

[@kristakingmath]

I'm so glad it helped!! Good luck on your midterm!

[@mommano]

A very simple and straightforward explanation. Thank you!

[@kristakingmath]

you're welcome! :)

[@cosmicjoshgaming3655]

3:24 why does the -x become x. You said that the negative goes away like how ? You didn't distribute the negative to -x or even used the ^2 . If you did use ^2 to make -x to x why is that -x has a ^2 (exponent) when you already used it

[@lumkanzwaki5555]

I know right?

[@kristakingmath]

You're welcome!! :) Hope they help!

[@Grassmpl]

Technically to test the "neither" case you should provide a counterexample by plugging in a specific value of x.

[@jangoodesai3962]

hi krista its good to learn from you explained it in an perfect manner as wanted tnkss a lot