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

► My Precalculus course: www.kristakingmath.com/precal...
Learn how to determine whether a function is an even function, an odd function, or neither an even nor odd function. We'll substitute -x for x, simplify, and then see whether our result is equal to our original function, and even, equal to our original function times -1, and odd, or neither.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.com/+Integralcalc/
QUORA // www.quora.com/profile/Krista-...

[@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

[@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! :)

[@kristakingmath]

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

[@sudarshanroxx]

❤️❤️❤️❤️Love From India❤️❤️❤️

[@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!

[@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

[@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! :)

[@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.

[@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

[@thiendo6647]

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

[@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 😃

[@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 😂😂😂

[@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!! :)

[@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!

[@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!

[@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

[@sefaa4089]

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

[@kristakingmath]

I'm glad I could help!

[@ThePerfect1077]

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

[@kristakingmath]

Thanks!

[@coldshot2112]

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.

[@kennethhowell5291]

Thank you! Your online math courses are the best!

[@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.

[@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.

[@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

[@kristakingmath]

I'm so glad it finally makes sense!! :D

[@bencarllson1475]

Thanks! this helped so much!

[@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!

[@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

[@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! 😀

[@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 ;)

[@jaymackyt2416]

You helped me past my final. Thankx

[@kristakingmath]

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

[@felixlokz]

I find it joyful watching your videos

[@jangoodesai3962]

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

[@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?

[@marathonpro92]

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

[@joel1544]

fail troll is fail

[@elizabethkaur7095]

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

[@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!

[@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.

[@bigjayfitness]

thank you you majestic wonder of the world

[@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

[@jetswhiteout961]

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

[@PokegurlMisty]

i am crying thank u for saving me

[@Bostonaustin25]

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

[@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!

[@IamArob0t]

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

[@kristakingmath]

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

[@IamArob0t]

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!

[@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

[@traveler8010]

explains better than my teacher!

[@kristakingmath]

thank you so much!

[@traveler8010]

C:

[@kristakingmath]

Awesome! Good luck on your test!! :D

[@baburo101]

love the precal videos... thanks a lot!

[@ourfutureisdark]

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

[@kristakingmath]

I hope you rock 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?

[@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! :)

[@andresb235]

Very helpful! you are one of my favorite youtubers YOU ARE AMAZING! THANKS

[@kristakingmath]

Aw thanks! 😊

[@anoirtrabelsi8645]

You can be a partner with Khan academy !!

[@kristakingmath]

That would definitely be cool! :)

[@rjlast2655]

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

[@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

[@kristakingmath]

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

[@coltonpicazo2922]

um cant really concentrate over how pretty she is.

[@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

[@BevDahBest]

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

[@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!

[@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?"

[@armandol5431]

Thank you Krista ! Clear and very helpful.

[@kristakingmath]

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

[@teresasanchez4771]

bro, I was so confused and this just helped tremendously!

[@JM995able]

You are awesome!!! This helped a lot to understand better the Fourier series. Thank you

[@peterdefelice2698]

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

[@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! :)

[@aewm96]

Really good video and very clear explaining, THANK YOU!!

[@kristakingmath]

You're welcome! I'm glad it could help.

[@Femiologist]

You just saved me for my CALC's class first quiz. I'm so happy I came across your video. :D

[@kristakingmath]

i'm so glad it helped!!

[@Shirtwithcracker]

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!

[@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! 😀

[@user-lf3wq3ii9k]

Thank you so much! I was really confused before! Watching the video helped me a lot!

[@kristakingmath]

I'm so glad it could help! Thanks for letting me know! :D

[@AnotherH8er]

Very fast and super easy to understand. Thank you for the help!

[@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

[@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.

[@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!

[@youtubetest3770]

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

[@kristakingmath]

Thank you very much!

[@gmzyymn2066]

All these videos you made are incredibly helpful ! Thank you so much :) Keep them up please for sake of all the math lovers ! :))

[@kristakingmath]

Aww thank for the comment! I'm so glad you like them! :)

[@samuelfauteux6735]

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

[@matw1matw152]

Actually this is the best explain I saw in my life , thank u continues

[@user-ec3rp2je6k]

excellent video! i was confused for so many hours, and you solved my problems in 4 minutes :)

[@mareasoceano5566]

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

[@kristakingmath]

+Mareas Océano I'm happy to help!

[@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.

[@priyapitre4468]

Thank you so much! I have been struggling in Calc for all this time, and finally I find something I get. Thank you so much :)

[@kristakingmath]

I'm glad I can help! :D

[@imanadil5849]

Thanks for this. i'm starting summer school in a week and this helps SOO MUCH!!!

[@kristakingmath]

I'm so glad it helped, and I hope summer school is going great! :D

[@kawasaki4life27]

thank you so much! you explain everything so clearly! keep up the good work!

[@abdikhadarhashi2357]

Thank u so much , I never understood this until I watched your video . I wish if math teachers can explain things like u do . Thanks again you are brilliant , I will follow your videos .

[@kristakingmath]

Thank you so much! I'm so glad this finally made sense! :D

[@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! :)

[@MrCompenso]

Your videos are great! Thank you so much for the work you do!

[@kristakingmath]

MrCompenso Thank you very much, I'm glad you like the videos!

[@jeffburdette2025]

Love your videos. Easy to understand

[@kristakingmath]

I'm so glad I could help! :)

[@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

[@kristakingmath]

Yay, I'm so glad I could help! :)

[@awesomenasam9180]

Hi...if there is a power like cos pow(7x) which type of fn it is

[@miguelarodz]

Thank you and it's really cool that you reply to everyone :-).

[@muhamedgamal1713]

hey , how to determine if the fn is even harmonic fn or odd harmonic fn "Fourier series"?!

[@kristakingmath]

I love the confidence! :D

[@orangemcnuggets]

Thank you very much! More power, and continue helping guys like us. :)

[@Grassmpl]

Yeah I wish her a power series with as much radius of convergence as possible.

[@dennisvijverbergbrakesrele6098]

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

[@BradKwfc]

So, I noticed the even one had an even exponent and the odd had an odd exponent. The one that was neither had two coefficients of opposite signs.....Would these rules work every time?

[@user-lf3wq3ii9k]

I think so. At least that's what my math teacher said. Though of course, you'd have to show your work.

[@crazedbrazy617bh]

Thank you it was helpful, always had a hard time with this, you made it simple

[@kristakingmath]

+crazedbrazy617bh You're welcome, I'm so glad it helped!