Transforming Algebraic Functions: Shifting, Stretching, and Reflecting 

I've been struggling to understand graphs all semester and you just explained it in 7 minutes, I actually love you

Brain.exe crashed, watched 4 vids today of your mathematics series. The highest i watched in one day. I have watched 65 vids so far. You are the one to be called a teacher. You have earned my respect sir. May Allah bless you!

Ur a beast...much better at explaining this concept than my teacher.

I'm in college algebra and I was seriously struggling with this. I did not get a good grasp from my professor. I watched videos from my online textbook, khan academy, and multiple random vids on youtube before I found yours. Thanks so much for the concise explanation!

I just finished my first night class for Pre-Calc30 and this video made everything we covered last night make a lot more sense. I really appreciate your efforts. I will watch more of your content as I am also upgrading my CHEM 30

Very simple and to the point. Thank you very much!

Thank you very much, professor dave. I’m watching a bunch of these videos to help me with my Algebra 1 class, as my teacher (and most US schools tbh) just teach “this is the formula, solve now” and not the actual concept in a way that’s easy to understand. Your videos make it a whole lot easier to grasp the concept of what all the x^2 stuff actually is doing to the function, and even made clearer what a function *is* . Thanks

I have seen many videos about this subject. Your explanation is the best ever. Thanks

An absolute genius! He deserves an AWARD!

In the final transformations table the horizontal shift is the other way around as stated during the video and the final comprehension exercises. A positive h means a shift to the left and a negative h a shift to the right!

I can’t thank you enough for simple methods

please keep making videos this is the only one I truly understood and I watched at least ten, in the future please add more examples just for reference

I can say that you and brian are really good at teaching, straight forward, you guys are the best

I so love this! On my way to understanding things! Thank you!! 🤗

Very clearly explained! A big thanks to you.

Thank you so much but you made a mistake in the summary of transformation for the h variable. Positive h= shift left, negative h= shift right . You’re the best❤

He is so much better than my Algebra teacher! Thanks for this lesson 🙂

Thanks Professor Dave

This is getting overwhelming right now Can't remember this much of concepts.

Not only super helpful but also has a kickass intro song. Wish I could give a super thumbs up

The whole video is summed up at 6:32

Bro you're here every time i need help bro... thank you so much

Wow this was awesome!! All day I was struggling to understand and this was so simple and informative. Thank you’

You saved my day, sir! I was struggling to understand this concept for my SAT prep, and search lot of YT tutorial but noc explain it like you. Take love, I am from Bangladesh!

Good video. I've read the order of operations matter when transforming functions. First we do the innermost parenthesis (horizontal shift) , then the horizontal/vertical stretches, and then the vertical shift. f(x) = -2(x - 3) ^2 +4 worked the way you did it, but there are cases where it won't.

This was mighty helpful, thank you so much!

THANK YOU THANK YOU THANK YOU U R A LIFE SAVERRRR I HOPE YOU HAVE AN AMAZING LIFE

your videos are awesome, keep the good work bro

i've never had problems with this concept but the way my teacher wants us to do it is so unreasonably complicated.

Another super great video!!! Thank you so much for creating these educational videos. They truly help. Thanks !!

Thank you for this Just one doubt What is the difference between vertical and horizontal stretch?

Difference between VS & HS: Narrows, less than/< 1 (will shrink), 1/2 (gets wider) - Vertical Stretch. If there's a coefficient inside with 'x' it's called - Horizontal Stretch Similarity between VS & HS: Both compresses and stretches depends on the symbol of [] 'a, b, c, d'

I saw 127 video in one day Completed playlist in 3 days

Wow I'm speechless. 👏

Ur a great man love ur videos keep uploading

I think you should always mention the order of transformations the same way you would do order of operations or the transformation could become messed up if you were to manually calculate it.

thanks a ton your vids help alot especially since ive been doing online school

oh, professor thanks. Actually I also really liked your videos in Astronomy.

Okay, can someone please explain the difference between the horizontal and vertical thingy for Dilation.

In the table, for horizontal shift-- positive h = shift to the lift instead of the right. Am I right?

Thanks! I made a special ‘cheat’ card from 6:28 to help me on transformations with my pre-calculus homework. I figured it didn’t have to be as complicated as many have been making it.

This video was really informative...thank you!

the best teacher ever

thank you

even after all this time this is video is very good

Very helpful video but on 3:39 you said horizontal stretch but you also said if it's better than 1 it's horizontal compress. Just check that keep up.

Hi, please correct the summary table: Horizontal shift part where negative h= is supposed to be to the right and positive h= shift left

thank you so much for this, such a wholesome video to learn! God Bless!

VERY useful and clear!! many thanks;

Awesome job professor Dave! Thanks

I only watch so that I hear the 'check comprehension' music.

You make it sound so easy as rare in a math teacher

I love it here.

It seems like the summary has some unintended mistake. You said that if h is negative, it should be shifted to right. But on the summary, it says that if h is negative, it should also shift to left. I'm confused, professor.

Thank you Professor

Keep it up 🙂

3:45 it's not a horizontal stretch but it's a horizontal shrink !!

im confused about the horizontal shift transformation on 6:28. I understood that (x+h) shifts left while (x-h) shifts right on the graph, or something I missed?

🥇

Thank you.

Is it "horizontal compress" at 3:37 instead of "horizontal stretch" as you say? Please check it up.

SO GOOD!

Thank you

Great work u man

Beauty of math.....😍😍😍

Great video

Nice video. It helped!

what would the transformation be for square roots such as 3square root x

Hello Professor Dave! Thank you so much for these valuable lessons! I have a question about the table @6:34. Isn't it supposed to read "positive h=shift left, negative h= shift right? Is there a typo or did I misunderstand something? Thanks again!

The page at 6:33 shouldn’t positive h= shift left not shift right same with nagative h should be shift right

is it inappropriate to call it 'horizontal compression', instead of stretch? or, is it requisite?

Professor Dave, the summary page at the ending of the video is incorrect for the horizontal shift. When it's a positive h, you shift left, not right. And when it's a negative h, you shift right; not left. Please read this guys!

thanks

Thanks man, it was life saving! At 6:30, you told, "+h = shift right, -h = shift left". Shouldn't it be "+h = shift left, -h = shift right"?

so positive and negative are opposites and shrink means to get wider and stretch means to get more narrow

you are the best

Yes

Would it be the same if you changed the f(x) part? Like if I have f(x+2)=x^2, would it be moved up? Also I love the outro music :>

Ur super sir... Love from Pakistan ❤❤❤

actually the conditions for streches are not expressed correctly. for example in 6:30 : a>1 is fine but a

nice video

honestly, I had no better explanation then this, if anyone is taking function or calculus, can we connect to help each other please, and thank you?

Is "f(x)=sqroot(x)" a valid fuction?. for every natural positive numbers besides 0 we will have two positive and negative outputs wich does not meet the "one output requierement". Also it would output imaginary numbers on the negative input side but i guess that wouldnt be a problem. Tahnk you Dave and thank you all the comunity!

best intro

Fuck imma fail this test tomorrow

how do u pick which numbers go under the x in the right column

6:30 - the positive h = shift right, negative h = shift left. I'm sure I'm missing something but isn't this the other way around?

sir, I'm lost at 4:42, if it's x cubed, then it means 2 x 2 x 2, right? can you sir tell me how did you get the 4, i'm really confused sir. Thank you in advance! :D

Dheivame 🙇

Shouldn't it střech horizontally too in the bottom example? It doesn't make sense to me :D 3:49

Wish i could found your channel more earlier 😊.

great video ! i have a question, if i have this function f(x) = 2^x + 3 and shifted left 8 units, stretched vertically, by a factor of 6, reflected about the x-axis , and then shifted downward 9 units , what would be the final function ? please help

How is it (-2)^3=8

DAVE!!!!!!! I LOVE YOU SO MUCH DADDY!!! YOURE SHIFTING MY FUNCTION UP RIGHT NOW 😏😏

Link to the "other strategies later in the series"?

My only criticizm about this one: I think you should've used more functions as an example, not just parabola. Perhaps, the sqrt(x) and maybe something else throughout all the transformations. Firstly, it would've demostrated the consistency of the methods as opposed to just ways to manipulate quadratic function graph specifically. Secondly, some of the transformations are confusing when applied to x^2 specifically because they render the same result or results with unobvious difference. For example, I was extremely confused with the stretch example: like, what's the difference between 4x^2 and (2x)^2, for example? Or the example of -x^3 and (-x)^3 was confusing, because you are, like, looking at it and wondering: ain't it the same thing (another example function where the distinction between the transformations would actually render the same result would've been great). Also, from your explanation of shifting along the x-axis, it wasn't clear at all how that would work with other functions (that's where the sqrt(x) example would be perfect). Also in my opinion, sin(x) is one of the best functions to show transformations on: I know that trigonometry hasn't been covered yet, but still, just saying.

do you have a link to ths powerpoint that I can print out. Your are so helpFUL thanks a bunch.

How bad is it that it took me 3 hours to fully get this 😭 am I cooked

When h positive doesn't the function shift left? and when negative to the right? isn't opposite what's on the table in the end?

For summary slide at 6:28 horizontal shift(h) shifts are opposite way round +ve is shift left -ve is shift right !! he said this in video but didn't correct it on this slide