Domain and Range Functions & Graphs - Linear, Quadratic, Rational, Logarithmic & Square Root

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  • เผยแพร่เมื่อ 21 ต.ค. 2024

ความคิดเห็น • 357

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  10 หลายเดือนก่อน +5

    Domain and Range Formula Sheet: bit.ly/4eheN2W
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

    • @abhigyansrivastava4247
      @abhigyansrivastava4247 2 หลายเดือนก่อน

      at 35:35 shouldn't it be negative infinity to positive 4 as domain

  • @brodyharlan1331
    @brodyharlan1331 5 ปีที่แล้ว +1172

    0:00 Intro + general rules
    12:57 Linear functions
    15:04 Quadratic functions
    21:17 Quadratic functions in vertex form
    23:08 Cubic functions
    25:00 Larger polynomials
    26:25 Square root functions
    37:21 Cubic root functions
    39:00 Quadratics under the radical
    44:05 Rational functions
    47:50 Square root in denominator
    51:42 Quadratics in numerator/denominator
    1:00:40 Absolute value functions
    1:02:30 Exponential functions
    1:05:38 Logarithmic functions
    1:11:38 Trigometric functions (sin + cos)
    1:15:30 Trigometric functions (tan)
    1:17:11 Conclusion

    • @sentinel_1752
      @sentinel_1752 5 ปีที่แล้ว +24

      the_brodes legend

    • @hannanbaig7888
      @hannanbaig7888 5 ปีที่แล้ว +10

      Salute to you the_brodes

    • @anandkumar-hn6wc
      @anandkumar-hn6wc 4 ปีที่แล้ว +3

      Thank you brodes

    • @moaadmustafa2233
      @moaadmustafa2233 4 ปีที่แล้ว +3

      why did u waste ure time doing this

    • @ashwinalagendran6748
      @ashwinalagendran6748 4 ปีที่แล้ว +30

      SuperiorTitanx he didn’t waste his time, he used his time to help us and that isnt viewed as a waste of time as he probably enjoys helping people

  • @younomehomie
    @younomehomie 6 ปีที่แล้ว +273

    im not saying khan academy is not good
    but the way you explain it is so much easier to understand then him
    thank you so much

    • @TheOrganicChemistryTutor
      @TheOrganicChemistryTutor  6 ปีที่แล้ว +100

      Thank you.

    • @larcous.7457
      @larcous.7457 4 ปีที่แล้ว +4

      same here

    • @smarti1144
      @smarti1144 4 ปีที่แล้ว +11

      it's more detailed. the Khan academy is kind of like a refresher or for those who have had one lesson already.

    • @Sweetysweets1999
      @Sweetysweets1999 4 ปีที่แล้ว +2

      True, tho I use khan academy as a refreshment before exams or a lecture or after I’ve studied the topic since they teach as if you have an idea of what the topic is about which I really like and is less time consuming (videos aren’t too long)

    • @tjdeguzman803
      @tjdeguzman803 3 ปีที่แล้ว +7

      @@TheOrganicChemistryTutor first time to see you replying haha

  • @dieformk
    @dieformk 4 ปีที่แล้ว +73

    i was struggling with domain for so long and this guy literally explained in less than 2 seconds. Amazing

    • @lancemesa6980
      @lancemesa6980 4 ปีที่แล้ว +6

      Fun fact: u lied, it cant be explained in less than 2secs lmao

    • @dieformk
      @dieformk 4 ปีที่แล้ว +11

      @@lancemesa6980 smh its an overexaggeration fool

    • @user-ki6pt2zg1h
      @user-ki6pt2zg1h 4 ปีที่แล้ว

      Watch this video examination in life never give up-th-cam.com/video/k4w4pak66V0/w-d-xo.html

    • @Keldrei22
      @Keldrei22 3 ปีที่แล้ว +1

      @@lancemesa6980 ikr stfu lance

    • @behailunadew6139
      @behailunadew6139 3 ปีที่แล้ว

      I was too

  • @ngwanesimwaba5550
    @ngwanesimwaba5550 3 ปีที่แล้ว +80

    You literally deserve awards for your brilliancy in your teachings not only for math but for all four sciences :)

    • @deceriejunsay4702
      @deceriejunsay4702 ปีที่แล้ว +1

      K😊😊🥊🥊😊😊😊🥞😊😊🍖😊🍖🍖🍞🍖🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊😊🥊🥊😊😊😊😊🥊🥊😊🥊🥊😊😊🥊

    • @deceriejunsay4702
      @deceriejunsay4702 ปีที่แล้ว

      K😊😊🥊🥊😊😊😊🥞😊😊🍖😊🍖🍖🍞🍖🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊🥊😊🥊🥊😊😊😊😊🥊🥊😊🥊🥊😊😊🥊

    • @deceriejunsay4702
      @deceriejunsay4702 ปีที่แล้ว

      55r41rqrq4444

    • @deceriejunsay4702
      @deceriejunsay4702 ปีที่แล้ว

      55r41rqrq444444f4

    • @deceriejunsay4702
      @deceriejunsay4702 ปีที่แล้ว

      E😊4

  • @Raevenswood
    @Raevenswood 6 ปีที่แล้ว +19

    seriously you are my go to guy for supplementing the lectures I get from my professor. sometimes he only can explain it one way but you seem to have a knack for connecting with my learning style. Just FYI your videos helped me get an A in Algerbra 1 last semester. Thank you.

  • @Pitiedowl
    @Pitiedowl 3 ปีที่แล้ว +7

    This dude is the first time ill actually support someone on patreon! count me in guru!

    • @prototype3162
      @prototype3162 3 ปีที่แล้ว

      i do too! i was always feeling to pay in a way back this dude for all the stuff i learned for free and when i found his patreon i didn t need it to think two times...

  • @juanthegodlyhorse6647
    @juanthegodlyhorse6647 4 ปีที่แล้ว +71

    35:42 - you should've written (-infinity , *+*4]
    BTW very nice teaching

    • @12framez60
      @12framez60 3 ปีที่แล้ว +3

      yo, that's right ! , i was about to type it when i found your comment

    • @Circa1628
      @Circa1628 3 ปีที่แล้ว +9

      @@12framez60 I know, I rewinded several times, thinking OH NO?! am i not understanding something. Almost went into a i'm-bad-at- math esteem spiral

    • @ngazibini.n2559
      @ngazibini.n2559 2 ปีที่แล้ว +5

      no the domain is correct. the graph is the one thats wrong. it all begins with the shifting, its shifted 4 units to the left so it begins at -4 not 4

    • @mansursaz1421
      @mansursaz1421 2 ปีที่แล้ว

      yeh

    • @OliviaRoedel
      @OliviaRoedel 8 หลายเดือนก่อน

      @@ngazibini.n2559 So I'm not saying your wrong, I'm just confused, because we solved for x making it x less than or equal to 4. Meaning it could be 4 and less. And then I look back at the original equation and y is negative and so it x, so therefore how would it be in any other quadrant. Can you more in depth explain where you got -4 from please and thank you.

  • @preciousx5181
    @preciousx5181 8 หลายเดือนก่อน +1

    Watching from Zambia, Thank you very much for this eye-opening lesson on functions.

  • @janetauseuga8951
    @janetauseuga8951 7 ปีที่แล้ว +213

    You have no idea how AWESOME you are!!!! (I'm sure you probably do, but)...THANK YOU! THANK YOU! THANK YOU! You explained it so well, that everything that I was confuse with, with most of my instructors, became so clear. Thank you.

    • @RupeshKumar-vq1vv
      @RupeshKumar-vq1vv 3 ปีที่แล้ว

      is it helping you now ..?? 😁 cz it's been 4 yrs ,

    • @ian.ambrose
      @ian.ambrose 2 ปีที่แล้ว

      @@RupeshKumar-vq1vv ? What do you mean

    • @ian.ambrose
      @ian.ambrose 2 ปีที่แล้ว

      @@RupeshKumar-vq1vv What you tryna say? What is your point bruh? Speak up

    • @RupeshKumar-vq1vv
      @RupeshKumar-vq1vv 2 ปีที่แล้ว

      @@ian.ambrose like what ? what are you asking about ? what you didn't got ?

    • @ian.ambrose
      @ian.ambrose 2 ปีที่แล้ว +1

      @@RupeshKumar-vq1vv Wanna fight?

  • @sadafsiddiqui9166
    @sadafsiddiqui9166 5 ปีที่แล้ว +12

    You are the only one who gives tons of example! Thank you!

  • @sweetness4j1
    @sweetness4j1 7 ปีที่แล้ว +89

    youre the reason i dont listen in class mate, i know that your videos always clarify things

    • @Aaron-v8m9j
      @Aaron-v8m9j ปีที่แล้ว +1

      Thats what fools do. They only rely on one person. You can still get invaluable information from your teacher and gain a more solid understading through different teachings. LOL about this comment.

    • @Aaron-v8m9j
      @Aaron-v8m9j ปีที่แล้ว +1

      And its you're, not youre, thats not a word.

    • @I-Fail-A-Lotl
      @I-Fail-A-Lotl ปีที่แล้ว +4

      ​@aaron9262 bro I wish that were the case for my physics class, teacher just bullies you 💀
      Though yeah paying close attention and taking notes on everything written is the way to go

    • @sekaopelaelo1934
      @sekaopelaelo1934 ปีที่แล้ว

      ​@@Aaron-v8m9j😂 but in the end you got what they meant 💀🤲

    • @ninabarakat6200
      @ninabarakat6200 ปีที่แล้ว

      @@Aaron-v8m9jIt’s “it’s”, not “its”; that word doesn’t make sense here. And since you want to be such a smart-ass, you comma spliced. dumbass kid

  • @mohammedsohailkhan1724
    @mohammedsohailkhan1724 2 ปีที่แล้ว +10

    Your work is ineffable! May God bless you and offer better rewards for all you consistent quality efforts... Thank you.

  • @tspizemediaservices6254
    @tspizemediaservices6254 4 ปีที่แล้ว +16

    Thanks my lecturer ...really appreciate this powerful knowledge. .much love from Zimbabwe!

    • @Aaron-v8m9j
      @Aaron-v8m9j ปีที่แล้ว

      cringe

    • @mcrshmelly
      @mcrshmelly 11 หลายเดือนก่อน

      @@Aaron-v8m9jget a job

    • @Someone-g5s
      @Someone-g5s หลายเดือนก่อน +1

      @@Aaron-v8m9j the fact that i see you in every freaking comment section...its giving obsession💀 get a life and don't comment "cringe" on a math video

  • @iradukundasolange7180
    @iradukundasolange7180 11 หลายเดือนก่อน

    Your way of teaching is very nice it isn't difficult to understand

  • @naomiduntin3298
    @naomiduntin3298 3 ปีที่แล้ว +1

    Is the voice for me so soothing an relaxing..Thanks for helping me understand maths.

  • @mirotransformers2012
    @mirotransformers2012 5 ปีที่แล้ว +18

    I really appreciate it bro , Now I know how to get the Range. I always used to get confused.

  • @gn3516
    @gn3516 3 ปีที่แล้ว +1

    You are the reason why i enjoy studying Math. Nobody else explain it how you do... STAY BLESSED!!!!!

  • @levi_ackerman824
    @levi_ackerman824 3 ปีที่แล้ว +9

    At 56:55 you wrote (-4,-7) instead of (-4,7). I was confused at first but then I understood. But thank you so much for this video. It helped me a lot :)

  • @pooransingh1882
    @pooransingh1882 ปีที่แล้ว +2

    An excellent lesson on analysis of functions. This would be a great help to students in university algebra.

  • @LauraTeAhoWhite
    @LauraTeAhoWhite 3 ปีที่แล้ว +5

    I feel like I just leveled up 10 points, this is amazing!

  • @gachiedr.
    @gachiedr. 2 ปีที่แล้ว +1

    Great, your methods are easily comprehensible.

  • @leenbaitalmal1583
    @leenbaitalmal1583 3 ปีที่แล้ว +16

    mistakes i noticed:
    35:42 - you should've written (-infinity , *+*4]
    42:00 D (-∞,-5⟧U⟦3,∞) are included for both -5 and 3

    • @Laithlaith-p6s
      @Laithlaith-p6s ปีที่แล้ว +1

      yes me to I find it mistake

    • @AhmedAMayow
      @AhmedAMayow 3 หลายเดือนก่อน

      -5 is not included because (x-3) substitute it gives you -8 but 3 is included.

    • @sarahjaneelumba9395
      @sarahjaneelumba9395 2 หลายเดือนก่อน

      ​@@AhmedAMayowthe input for the x-3 doesnt really matter if the difference of the other equation is 0

    • @sarahjaneelumba9395
      @sarahjaneelumba9395 2 หลายเดือนก่อน

      thus, anything that gets multiplied by 0 will be 0 and that aint no undefined for radicals

  • @Thanatoos
    @Thanatoos 2 ปีที่แล้ว

    this guy literallt teachea us for 1hour straight.
    i am greatful for this guy.

  • @lune1469
    @lune1469 3 ปีที่แล้ว +3

    Literally blessing in disguise! Thank you sooooo much! 💜

  • @Someone-g5s
    @Someone-g5s หลายเดือนก่อน

    THANK YOU SM YOUR A LIFE SAVER (ima go tell all my friends about your channel)

  • @mashaeldosari7428
    @mashaeldosari7428 4 ปีที่แล้ว

    This channel is why I got an A in physics last year and now it's helping with my advanced classes

  • @VsroYT
    @VsroYT 5 ปีที่แล้ว +4

    GET THIS MAN TO 1 MILLION SUBSCRIBERS
    HE DEFINITELY DESERVES IT!

    • @mughira1012
      @mughira1012 4 ปีที่แล้ว +1

      Well I've got some good news for you he's currently at 2 million subscribers!

    • @mcrshmelly
      @mcrshmelly 11 หลายเดือนก่อน

      @@mughira10127 mil now

  • @hillalworldly732
    @hillalworldly732 4 ปีที่แล้ว +1

    Thank you, I won't forget the day I found your channel, I just want to tell you that you helped many students so you have to proud of yourself 😉

  • @kasuyp
    @kasuyp 5 ปีที่แล้ว +4

    Thank you very much.. I am a math teacher but I really find your tutorial videos helpful on how to make the topics in math easier for the students.. Godbless brother

  • @rukasihyogaswara6913
    @rukasihyogaswara6913 4 ปีที่แล้ว +1

    Very big thank you.....!!!!! Stay healthy, God bless you

  • @korezua12
    @korezua12 3 ปีที่แล้ว +4

    If you are searching for 15:50
    Yes, he meant the "exponent", not the leading coefficient.
    You're welcome

  • @phucdangchannel
    @phucdangchannel 6 ปีที่แล้ว +17

    I'm so glad i don't live in the older generations where the internet did not exsist

    • @SM-qn7sr
      @SM-qn7sr 3 ปีที่แล้ว

      My cousin had to buy math books for dummies to understand each lecture lmaoo

  • @knightn-i-nja5950
    @knightn-i-nja5950 7 หลายเดือนก่อน

    Thank u sooooooooooooooooo much sir
    I'm sure I'm gonna score full mark thanks to ur video i just come back to say tht I wish u the best year❤

  • @todayiglowup4286
    @todayiglowup4286 6 ปีที่แล้ว +5

    u are a fucking life saver bro, ur video was the perfect thing i needed to review all my domains and ranges. like literally u have no idea how grateful i am to you

  • @rhyolitee
    @rhyolitee 6 ปีที่แล้ว +4

    Thank you so much, you make it very easy to understand the concepts being taught.

  • @alifupm1803
    @alifupm1803 4 ปีที่แล้ว

    thank you , you are my lifesaver .. pray for my 1st semester test next week ;)

  • @ms.mysterious7474
    @ms.mysterious7474 6 ปีที่แล้ว +5

    This cant get any better

  • @vinitagarwal5767
    @vinitagarwal5767 2 ปีที่แล้ว

    Amazing bro, you explain so easily and make it simple, perfect

  • @sappy2079
    @sappy2079 ปีที่แล้ว +1

    You made my grade 11 math way too easy

  • @abhinaysinha5313
    @abhinaysinha5313 6 ปีที่แล้ว +2

    Please make a video on how to find the range of a function your videos are very helpful for children who are going from 11th and 12th class

  • @parakhsharma429
    @parakhsharma429 6 ปีที่แล้ว +1

    you are making education so easy thank you very much

  • @khalifaharuna9852
    @khalifaharuna9852 5 ปีที่แล้ว

    words can't describe how helpful you are. Thanks.

  • @nchimunyabukoole5876
    @nchimunyabukoole5876 5 ปีที่แล้ว +4

    I always find what I need from you, thank you, you have nice explanations

  • @waheedshersher8217
    @waheedshersher8217 6 ปีที่แล้ว +43

    in the minute 35.31 the domain is (-infinity, +4]

  • @niaris111
    @niaris111 5 ปีที่แล้ว +2

    this guy saves lives.

  • @aicellecawili1267
    @aicellecawili1267 3 ปีที่แล้ว

    Hi! Can you be my regular tutor :) coz youre an AWESOME TUTOR that I like especially when it comes in Math.:) thank you

  • @aesthete8237
    @aesthete8237 4 ปีที่แล้ว +2

    Sir I just want to correct the little mistake on your last example for quadratic function. It should be positive 7 instead of negative 7.
    But great, great, great video Sir. I salute and admire you alot
    Have a nice day

  • @MrNorthDraws
    @MrNorthDraws 7 ปีที่แล้ว

    Your videos are the best on you tube.

  • @nathanielsteviedandradecar8287
    @nathanielsteviedandradecar8287 6 ปีที่แล้ว

    This guy is the goat. Thank you.

  • @gloooopgloop
    @gloooopgloop 8 ปีที่แล้ว +50

    Tip after watching this video- Add time straps in the description

    • @chin5983
      @chin5983 7 ปีที่แล้ว +1

      Yeah I need that

  • @AsimAli-gj5wp
    @AsimAli-gj5wp ปีที่แล้ว

    it is more than helpful.. THANK YOU

  • @hexigin8695
    @hexigin8695 2 ปีที่แล้ว +1

    This man is carrying my grades rn

  • @abhishekkulkarni7057
    @abhishekkulkarni7057 7 ปีที่แล้ว +3

    this guy is a legend

  • @sneipstylive8325
    @sneipstylive8325 3 ปีที่แล้ว

    He is so much better at teaching this than teachers.. no offense teachers

  • @GhostHacker97
    @GhostHacker97 5 ปีที่แล้ว +1

    This clarifies so much thanks!

  • @brwashkurismail2556
    @brwashkurismail2556 4 ปีที่แล้ว

    i understand you better than our teacher on school

  • @samarthsubbaraomullapudi7304
    @samarthsubbaraomullapudi7304 4 ปีที่แล้ว

    You are one of the best - and I have learnt a lot from you.

  • @khymjubindultra457
    @khymjubindultra457 4 ปีที่แล้ว

    THANK YOU VERY MUCH MAN, OUR PRELIM IS TOMMORROW. YOU HELPED ME A LOT, FOREVER GRATEFUL TO THIS TH-cam CHANNEL :D :D (y) (y)
    I SUBSCRIBED

  • @g.a.2416
    @g.a.2416 4 ปีที่แล้ว +6

    56:54 is (-4,7)

  • @zazaza5535
    @zazaza5535 ปีที่แล้ว +1

    Closed circle refers to 'equal to', an open circle refers to 'greater or lesser than'.

  • @AdityaSingh-ml9wn
    @AdityaSingh-ml9wn 2 ปีที่แล้ว +1

    At 41:57 you should have put closed brackets around -5 and 3 as they can be included

  • @georgeedward9271
    @georgeedward9271 3 ปีที่แล้ว

    This teaches me more than a math lecture from my teacher

  • @wizyoni3217
    @wizyoni3217 2 ปีที่แล้ว

    You have no idea how AWESOME you are💯💯💯

  • @enasgeravi4372
    @enasgeravi4372 2 ปีที่แล้ว +1

    شكرا و جزاك الله خيرا

  • @yeeunpark8291
    @yeeunpark8291 2 ปีที่แล้ว

    Your just awesome math teacher

  • @hopeforall-mp9db
    @hopeforall-mp9db ปีที่แล้ว

    U are such a blessing

  • @sarahle7160
    @sarahle7160 4 ปีที่แล้ว

    Thanks God... This is so much easier to understand than my teacher...He has spent for 3 days for teach it...

  • @r.n3838
    @r.n3838 5 ปีที่แล้ว +1

    Great teaching

  • @tamaghnadey3050
    @tamaghnadey3050 3 ปีที่แล้ว +1

    The vertical asymptote for the last question would be R - {x:x=(2n+1)*π/2, n ε Z, x ε R}

  • @David-ob1so
    @David-ob1so 4 ปีที่แล้ว

    30:00 is what i needed thanks

  • @shashwatkumar6248
    @shashwatkumar6248 4 ปีที่แล้ว

    You teaches better than allen coaching institute digital classes

  • @mirazreigns6048
    @mirazreigns6048 6 ปีที่แล้ว

    I'm watching from bangladesh...it is very very helpful for us...I've many problems on functions I didn't understand that...but now it getting much imoroved...thank you sir......

  • @TimMorris1
    @TimMorris1 4 ปีที่แล้ว +1

    I'm so happy I found your channel. It's helped me so much. Thank you !

  • @muhammadhadi9390
    @muhammadhadi9390 2 ปีที่แล้ว

    Thank you very much. This really helped me

  • @ゴロゴロ素人
    @ゴロゴロ素人 2 ปีที่แล้ว

    I’m Japanese high school student. In Japan, we learn things about functuons like this video when we are 16 years so I think Japanese education is advanced.

    • @hi-ib6es
      @hi-ib6es ปีที่แล้ว +1

      in the usa i learned this at 15

    • @multimeme5935
      @multimeme5935 8 หลายเดือนก่อน

      no you are not.

  • @waheedshersher8217
    @waheedshersher8217 6 ปีที่แล้ว

    this video is amazing, I feel proud to listen to your videos man.

  • @jamesedwardtagalan2147
    @jamesedwardtagalan2147 3 ปีที่แล้ว +1

    Thank you so much Sir!

  • @bogadipoloko2679
    @bogadipoloko2679 5 ปีที่แล้ว +1

    such a live saver

  • @hamayoonshah1990
    @hamayoonshah1990 2 ปีที่แล้ว

    The name of this channel should be “the one man army in every field”

  • @ms.mysterious7474
    @ms.mysterious7474 6 ปีที่แล้ว +14

    I'm seriously praying for u

  • @paulneale614
    @paulneale614 3 หลายเดือนก่อน

    Love your videos they are brilliant, have you a complete algebra 2 course I could buy

  • @anandkumar-hn6wc
    @anandkumar-hn6wc 4 ปีที่แล้ว +1

    Thank you very much sir.

  • @giemarcabreros6133
    @giemarcabreros6133 4 ปีที่แล้ว

    its very nice video,i learn a lot

  • @mohdshayril9038
    @mohdshayril9038 7 ปีที่แล้ว +6

    The reason i can sleep in my math lecturer's class LOL..
    Thanks for great video btw ,keep it up !

  • @AbdulAziz-gz3wy
    @AbdulAziz-gz3wy 3 ปีที่แล้ว +1

    I am from Yemen....My name is Abdulaziz...I don't speak English but the numbers are easy....I want to learn....

  • @shubhang2021
    @shubhang2021 5 ปีที่แล้ว +1

    Thanks..keep making such videos

  • @katecallao5758
    @katecallao5758 4 ปีที่แล้ว +1

    My math teacher works hard but The Organic Chemistry Tutor works harder oWo

  • @paulgeorgemuntean4186
    @paulgeorgemuntean4186 6 ปีที่แล้ว +9

    At 41:52 the D (-∞,-5⟧U⟦3,∞) are included for both -5 and 3?

    • @georgewong6312
      @georgewong6312 5 ปีที่แล้ว +5

      Happy to see this. Scrolled to see if my answer is the same with others.

  • @mr.nobody8958
    @mr.nobody8958 7 ปีที่แล้ว +6

    Man you're great but I think u should try to make your videos more sorts because it's looks like a lecture!

    • @Ms452123
      @Ms452123 6 ปีที่แล้ว +13

      The length is what makes it good, everyone else makes short videos that don't cover enough examples. How can you complain about more content? You can easily watch as much as you like then leave the rest for a later day.

    • @phucdangchannel
      @phucdangchannel 6 ปีที่แล้ว +3

      The longer the better.What you come here on youtube for a 5 minute youtube video?For example you have a cal 3 test and how good is 5 minutes or 20 minutes going to do you?Think about other people as well.they need this too.

    • @SM-qn7sr
      @SM-qn7sr 3 ปีที่แล้ว

      I actually like it when he makes comprehensive, long thorough videos

  • @MrsKobes
    @MrsKobes 4 ปีที่แล้ว

    YOU ARE THE BEST!

  • @moazmizan7576
    @moazmizan7576 4 ปีที่แล้ว

    Ohh how he is so calm and cool

  • @pauljhonanthonypitogo7387
    @pauljhonanthonypitogo7387 6 ปีที่แล้ว

    THANK YOU FOR THIS VERRY AWESOME VIDEO !!

  • @jenilshah2231
    @jenilshah2231 4 ปีที่แล้ว +1

    Books preferable for such questions?

  • @anshubist5316
    @anshubist5316 6 ปีที่แล้ว

    Thank u sooo much sir....very effective teaching .. thank uuuuu

  • @ianjoseph5325
    @ianjoseph5325 11 หลายเดือนก่อน +1

    I know it is kinda late but in minute 41:50 isn't the domain suppose to be D[3,positive infinity) since the value of the equation is greater than or equal to zero so -5 is not included?

  • @hamdan9268
    @hamdan9268 ปีที่แล้ว +1

    35:24 domain should be (-infinity,4] rather than -4

  • @alvinali2425
    @alvinali2425 ปีที่แล้ว

    Kendrick might not be my savior but you are😂❤

  • @congtruong767
    @congtruong767 5 ปีที่แล้ว +1

    Such a great video). Thank you sooooooooo much:)

  • @sadafanwar9278
    @sadafanwar9278 3 ปีที่แล้ว

    best explanation