Transformations of Functions | Precalculus

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  • Опубліковано 4 лют 2025
  • This precalculus video tutorial provides a basic introduction into transformations of functions. It explains how to identify the parent functions as well as vertical shifts, horizontal shifts, vertical stretching and shrinking, horizontal stretches and compressions, reflection about the x-axis, reflection about the y-axis, reflections about the origins and more. Parent functions include absolute value functions, quadratic functions, cubic functions, and radical functions. This video contains plenty of examples on graphing functions using transformations.
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    Direct Link to The Full Video:
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    Functions - Free Formula Sheet:
    bit.ly/3Ai8NZv
    _________________________________
    Full 53 Minute Video:
    • Transformations of Fun...
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КОМЕНТАРІ • 289

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +40

    Functions - Free Formula Sheet: bit.ly/3Ai8NZv
    Get The Full 53 Minute Video: www.patreon.com/MathScienceTutor
    Direct Link to The Full Video: bit.ly/38smJyA
    Functions - Video Lessons: www.video-tutor.net/functions.html

  • @Justin-ny8df
    @Justin-ny8df 3 роки тому +709

    My lecture was 2 hours on the same topic you did in 22 minutes. I highly appreciate your work.

  • @jeccamapagdalita9050
    @jeccamapagdalita9050 3 роки тому +973

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    • @that_off
      @that_off 3 роки тому +31

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      @nicole.a2694 3 роки тому +10

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    • @stylejitsu9125
      @stylejitsu9125 2 роки тому +35

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  • @ddahstan6876
    @ddahstan6876 3 роки тому +136

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  • @levixhange7989
    @levixhange7989 3 роки тому +75

    I'm sobbing right now. You don't know how relieved I am. We have problems like these in our activity and our prof didn't mentioned those in the files that he gave. Thank you so much!

  • @oelfajri
    @oelfajri 3 роки тому +233

    I don't know how you can be more helpful than my math professor. I really appreciate this.

  • @parth7531
    @parth7531 2 роки тому +43

    Bro you don't even realise that you have provided so much indepth knowledge to so many people of multiple topics, due to which they are able to well perform in their exam. salute you man

    • @AcidDaBomb
      @AcidDaBomb 5 місяців тому

      Been in college for a few years, he's the reason why my GPA is above 3.5

  • @elenaivoy
    @elenaivoy 3 роки тому +37

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  • @bozo7545
    @bozo7545 3 роки тому +371

    At the moment, I’ll likely won’t need to use this video as I will not be starting my math course until the end of April, but I just wanted to say that I hope you’re doing well and thank you again for helping out countless viewers :)
    Update: Currently needing this specific video for Unit 3 of my math course!

    • @lemniscatel5491
      @lemniscatel5491 3 роки тому +13

      Just finish the video now instead of postponing it lol

    • @16piecemcnuggetmeal18
      @16piecemcnuggetmeal18 3 роки тому +2

      ayo u doin quads too

    • @bozo7545
      @bozo7545 3 роки тому +9

      @@16piecemcnuggetmeal18 at the moment I’m currently doing trigonometry relating to radians and unit circles :)

    • @noramay6049
      @noramay6049 3 роки тому +1

      you do maths methods?

    • @awesomedarkstalker4991
      @awesomedarkstalker4991 3 роки тому +1

      @@bozo7545 precalculus 12?

  • @OwdeeTeeTee
    @OwdeeTeeTee Рік тому +27

    I have the utmost gratitude for the impeccable videos that you make. You literally make math significantly less frustrating and (almost) fun lol. I am struggling to get through my last college math course and following your videos makes it that much more bearable. Thank you JG, you are the Master Jedi of math.

  • @braileythompson3217
    @braileythompson3217 2 роки тому +47

    You save my life in ALL of my classes. Thank you for being an amazing teacher!!

  • @that_off
    @that_off 3 роки тому +9

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  • @ramyaj1693
    @ramyaj1693 2 роки тому +6

    Thank you so much. For some reason, watching my class recordings multiple times didn't help me as much as your videos. I went from 59/100 to 72/100.

  • @VinceVintage
    @VinceVintage 3 роки тому +86

    OMG I needed this!! My online algebra class is using a 11 year old youtube video that SUCKS compared to this
    Your explanation is amazing! Thank you for your work

    • @vukxia5567
      @vukxia5567 2 роки тому

      Were u using acellus?

    • @momentomoriwrath
      @momentomoriwrath 2 роки тому

      didn’t expect to see you here, why are in an online algebra class? fire videos btw, subbed a min ago.

  • @PeaceAndProgress1242
    @PeaceAndProgress1242 2 роки тому +11

    21:18 "My graph is not perfect but you get the point." Masterful pun 👏👏

    • @MillionaireMael
      @MillionaireMael 2 роки тому

      18:04 wouldn’t the 3 shift to the left?

    • @somxr_738
      @somxr_738 Рік тому +1

      @@MillionaireMael No that’s incorrect. 3 is positive so it’s to the right

  • @elidahmichellesupero9253
    @elidahmichellesupero9253 3 роки тому +6

    You are a life saver , you don't know how much your videos has seen me through my exam preparations

  • @zynx31
    @zynx31 2 роки тому +5

    I just wanna say this is the second time you saved me! First was chemistry and now math. I really appreciate your work, You explained everything so well and clearly. I was working on a problem for hours and not getting it, but after watching your video I finished all the problems within 20 minutes. you explained it so much better than my teacher LMAO! Thank you so much I appreciate your work!

  • @cameron9915
    @cameron9915 3 роки тому +9

    I hate my textbook so I just searched you up for help as usual. Always a great help, thank you.

  • @skzbits-rh9xh
    @skzbits-rh9xh Рік тому +1

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  • @majestichellium9166
    @majestichellium9166 2 місяці тому

    You just saved me hours of rewatching my math classes I really appreciate you making these videos

  • @platformofscience9790
    @platformofscience9790 3 роки тому +78

    It's amazing that you're back again.

  • @MsHortel
    @MsHortel 11 місяців тому

    I ❤ all his lectures. It is like a magical therapy for my brain and emotions. It gives me confidence and cures my math trauma.😂😂😂

  • @redsun5826
    @redsun5826 3 роки тому +26

    oh i get it now!!!! thank you so much!!!! i’m pissed that i missed this one on the exam because i had a weak understanding of it. my professor didn’t explain it thoroughly like you did! ugh, i’m gonna be referring to your videos next time my professor’s lectures are lacking!!

    • @that_off
      @that_off 3 роки тому +2

      ikr, he's the best

    • @mero9096
      @mero9096 2 роки тому

      haha faced the same problem today! my exam would’ve gone so much better if i had had a more solid understanding of these transformations. glad i found this video so i don’t make those same mistakes again

  • @georgesadler7830
    @georgesadler7830 3 роки тому +7

    MR. Organic Chemistry Tutor, thank you for another monster video/lecture on Transformations of Functions. Graphs recognitions are very helpful when learning Transformations of Functions.

  • @___Archangel____
    @___Archangel____ 3 роки тому +8

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  • @dirkdiggler2218
    @dirkdiggler2218 Рік тому

    I've understood more from watching this for six minutes than I have from staring at the file my professor gave me for two hours. sheeeeeesh!

  • @rajveerbhardwaj8470
    @rajveerbhardwaj8470 3 роки тому +14

    Here to study for my Pre-Cal test tomorrow thank you.

    • @Evine39
      @Evine39 3 роки тому

      Same here.

    • @destinygibson5671
      @destinygibson5671 3 роки тому

      same

    • @navi3430
      @navi3430 3 роки тому

      How did it go?

    • @destinygibson5671
      @destinygibson5671 3 роки тому

      @@navi3430 unfortunately i only got a 75, but i believe if you have a test you’ll do better

    • @navi3430
      @navi3430 3 роки тому +1

      @@destinygibson5671 I’m trying my best in Precalc right now. It’s not going very well.

  • @darkhumor7256
    @darkhumor7256 2 роки тому +8

    I love this man, you make it so easy to learn . Thanks you are the reason I'll be graduating in a few months

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    @abdullahraajput500 3 роки тому +13

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  • @Monster_Face_RB
    @Monster_Face_RB Рік тому +1

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  • @tary_233
    @tary_233 3 роки тому +3

    Thank you for helping. I have an exam in a few hours and you have been of so much help sir

  • @chewbleu
    @chewbleu 3 місяці тому +2

    Best channel on youtube

  • @leap352
    @leap352 2 роки тому

    My teacher has been explaining this lesson for a week and kept ignoring my questions so thanks for actually helping since i've got a quiz on it.

  • @AaravR._
    @AaravR._ 4 місяці тому

    love your math content, omg im studying last min and its so helpful even without audio

  • @mbuc4498
    @mbuc4498 11 місяців тому +1

    My exam Is tonight and I've learned more 12 minutes into the video than my instructor has taught in 6 weeks. Im watching all these videos hope I can pass ;)

  • @Niiki030
    @Niiki030 Рік тому

    you teach better than my precalc math teacher EVER could.

  • @soenhou2845
    @soenhou2845 2 роки тому +1

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      @AV-wx3yx 3 роки тому

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  • @quackkuryu4680
    @quackkuryu4680 3 роки тому +13

    your videos are so good. why do teachers make things so complicated?

    • @abc-xn4fj
      @abc-xn4fj Рік тому

      hhh

    • @wx111.
      @wx111. Рік тому

      exactly.. watching this it seems hard but so much simpler than what my teacher is teaching in class… like really its frustrating!!

  • @jestphoenix
    @jestphoenix 3 роки тому +1

    i'm a freshman but my teacher is making us learn some precalc stuff so... tysm i have eocs tmr and am currently cramming

  • @AlexMoreno-s5h
    @AlexMoreno-s5h 3 місяці тому +1

    Hate to say it but you explained better than my high school teacher

  • @12degreesnowman11
    @12degreesnowman11 2 роки тому +2

    Thank you 😭 I have learned transformations

  • @yourtubersdanceteam
    @yourtubersdanceteam Рік тому

    I wacth towns of your videos and help me alor and recommended to almost all my friends and they find it useful and my school has aks me if I want to be math tutor in math class that was all bc of you

  • @akhilnalajala7661
    @akhilnalajala7661 4 місяці тому

    This was the most helpful and easy video i could find! Thanks!

  • @Velas99
    @Velas99 Рік тому

    Thank you so much for your help JG. Quick questions. When you are altering the x values for the horizontal transformations (11:00 minute) do you apply the reciprocal of 2 and 1/2 to get the new values of x?

  • @ARSHDEEPSINGH-rd2ob
    @ARSHDEEPSINGH-rd2ob Рік тому

    i am so grateful that you exist

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    @angelogarofalo4932 3 роки тому +4

    This mans doing God's work I swear

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    @Lovely_Gire 2 роки тому

    This is the only lecturer that I understand

  • @anthonygomez2900
    @anthonygomez2900 2 роки тому +2

    Omg you literally saved me from failing my algebra test thank you

  • @dezvaldez143
    @dezvaldez143 Рік тому

    U make this easy, and effortless...Bravo😊

  • @tatehearst
    @tatehearst 4 місяці тому

    I have a quiz on this tomorrow!!! Hopefully this video helps meeee

  • @brian-a678
    @brian-a678 10 місяців тому +39

    who makes these rules

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    @KateVwalika-th6tf Рік тому

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  • @Hero-el5gi
    @Hero-el5gi 2 роки тому +1

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    I hope to get excellent grades

  • @radioheadfan56
    @radioheadfan56 7 місяців тому +1

    thanks man my teacher sucks and this helped sm

  • @sgtdeven6452
    @sgtdeven6452 3 роки тому +1

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  • @mistermeer
    @mistermeer 3 місяці тому

    Thank you. You saved my Life.

  • @aashrithavula2586
    @aashrithavula2586 Рік тому +1

    Great video you really helped me understand the concept thanks
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  • @kevinlee2606
    @kevinlee2606 2 роки тому

    Your voice is so calming

  • @lauhityaaashwinkumar
    @lauhityaaashwinkumar 4 місяці тому

    Thanks a lot bro, this cleared all my doubts. ❤

  • @EmpyreanLightASMR
    @EmpyreanLightASMR 3 роки тому +3

    I never did well in algebra (I was good at geometry and decent at trig) but the word "pre-calc" scared me, so I stopped math courses and I'm regretting it now. I make the same mistakes in algebra that I did as a kid, which I found interesting, so I need to slow down and try to be smart about things. but other than that, I really enjoy pre-calc. May have to brush up on all the Trig I can before moving on to Calculus.

  • @leiakates1745
    @leiakates1745 3 роки тому +2

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  • @AnupamaDewmith
    @AnupamaDewmith 19 днів тому

    you are saving lives💙

  • @DanielWilschetz
    @DanielWilschetz Рік тому +3

    For the last problem, why does it go right 3 and not left 3?

  • @AnthonyHousen-vv7go
    @AnthonyHousen-vv7go 9 місяців тому +2

    im confused about 18:13. if (3-x) =+3 that would a horizontal shift to left 3 why is the square root of 3-x which is +3 not also a horizontal shift to the left ?

    • @mkn-0412
      @mkn-0412 4 місяці тому

      take (x+3) as an example, normally you will say it a horizontal shift to the left, right?
      so it is bc x + 3 = 0 x = -3 is a negative shift
      so, the same with 3-x; 3-x = 0 only when x = 3 which is a positive, so we have a horizontal shift to the right

  • @cloudiimind222
    @cloudiimind222 10 місяців тому

    This actually helped so much , U DA BEST SIR

  • @Joyzkiee
    @Joyzkiee 2 роки тому

    Boh my teacher in Math and science, used your video for their lecture

  • @taker44
    @taker44 2 роки тому

    Thanks very mush the greatest teacher of all time❤

  • @abby-9921
    @abby-9921 3 роки тому +1

    words cannot express how much you save my ass every week

  • @ay3ron
    @ay3ron 6 місяців тому +2

    19:37 I thought whatever was in the bracket of x, the number inside is the opposite of what the horizontal translation taking place -- shouldnt this be a horizontal shift to the left ? Could someone help me

    • @ranonymous27
      @ranonymous27 6 місяців тому

      did u get it?

    • @ay3ron
      @ay3ron 6 місяців тому

      ​@@ranonymous27 yes

    • @ay3ron
      @ay3ron 6 місяців тому

      ​@@ranonymous27actually I don't get it

  • @amogus-vt7pg
    @amogus-vt7pg Рік тому

    this man is a legend

  • @Mr_Nobody66273
    @Mr_Nobody66273 2 роки тому

    I dare UA-cam to show me a better teacher

  • @visoren6580
    @visoren6580 3 роки тому +3

    Thank you so much man, you've helped me out so much! :)

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    @ducklover200 Рік тому

    you’re a lifesaver

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    @isaiahestilien4531 Рік тому

    You have been such a great help for me, thank you

  • @Yalda_ebrah
    @Yalda_ebrah 11 місяців тому +2

    I love your voice ❤😢

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    @park7221 Рік тому

    u just saved my life

  • @breakdown1015
    @breakdown1015 3 роки тому +2

    watched this 30 mins before my test after not knowing anything, let’s see how this goes

  • @twentysecondcenturywoman
    @twentysecondcenturywoman 29 днів тому

    Thank you so much for your videos.

  • @jan-willemreens9010
    @jan-willemreens9010 3 роки тому +2

    SQR(2x) can also be written as SQR(2)timesSQR(x) according to the rules, am I right? So, doesn't this mean a vertical stretch of SQR(2)(>1) beside a horizontal shrink? It is not yet clear to me that people only describe this function as a horizontal shrink! thanks in advance for your attention...

  • @Eldiosqueprovee
    @Eldiosqueprovee 3 місяці тому

    Lo and behold the prodigy of math

  • @MillionaireMael
    @MillionaireMael 2 роки тому +5

    18:04 wouldn’t the 3 shift to the left?

    • @zigglyz7120
      @zigglyz7120 Рік тому

      Yeah. I was also thinking the same as we can take f(×)=(-x)½ then (-x+3)½can be written as f(x+3) which should shift towards left.
      Right????

    • @aviiamo
      @aviiamo Рік тому

      yesss it should go to the left

    • @aviiamo
      @aviiamo Рік тому

      BUT ITS TO THE RIGHT ON DESMOS TOO WHTS GOING ON

  • @Whiteszeee
    @Whiteszeee 4 місяці тому +14

    My math test is in 1hour.

  • @marshmallow1553
    @marshmallow1553 Рік тому +1

    Maths is so hard, but I have to try my best to get it right, my final end year exams will decide my college/university , hopefully I can get an A1 or at least A2, lololol
    But I should at least try to pass my maths first

  • @aleezysleezy
    @aleezysleezy Рік тому

    you are so so so helpful THANK YOU

  • @dreams5672
    @dreams5672 Рік тому +1

    He ate with this tutorial

  • @Ayalt61
    @Ayalt61 3 роки тому +1

    you're amazing thank you so much I really appreciate this :)

  • @bradking6902
    @bradking6902 3 роки тому +24

    You should be getting some form of compensation from the university lecturers we are all not using lol

  • @Zconceited_
    @Zconceited_ 2 роки тому

    Tysm this has made my hs freshman year stressful

  • @sss-mr1hc
    @sss-mr1hc 2 місяці тому

    For dilation when it's horizontally stretching or shrinking Do we need to multiply with the x value only? I don't understand

  • @krispy5171
    @krispy5171 21 день тому +1

    Revising this before exams even tho I know I’m cooked

    • @sunnyvioletz
      @sunnyvioletz 21 день тому

      same as me, godspeed to both of us 😭

  • @PovaSlemani
    @PovaSlemani Рік тому

    Thank you tacher i understood now❤

  • @thecenteroftheuniverse6982
    @thecenteroftheuniverse6982 2 роки тому

    what do you use to make these videos? a tablet or something?

  • @broker17-u9t
    @broker17-u9t 11 місяців тому

    I SWEAR you need to GET the NOBEL PRIZE!!! You share knowledge for free !!!!! Great mathematicians, physicists,chemists and all Great Scientific persons would put you in the Pantheon for the progression of science!!!!

  • @arjunghartiarjungharti
    @arjunghartiarjungharti Рік тому

    Thank you so much sir ❤❤😊😊💗🌷💝💖

  • @ngonggai2309
    @ngonggai2309 3 роки тому +1

    Thank you bro, you are amazing.

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    @dewyy4168 3 роки тому

    You’re the reason I’m passing cyber

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    @IMMXSTXRR Рік тому +32

    Jesus loves you

    • @Zeegycel
      @Zeegycel 4 місяці тому +3

      I needed that ❤

  • @givemebeidou2446
    @givemebeidou2446 3 роки тому

    this video was so helpful... thanks sm
    p.s. not relevant but ur voice sounds like albedo from genshin impact

  • @lesterbialog8523
    @lesterbialog8523 2 роки тому +1

    Your voice sounds like I'm gonna have an A+ in math.