Transforming Algebraic Functions: Shifting, Stretching, and Reflecting
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- Опубліковано 5 лис 2017
- Now that we know the basics regarding graphing algebraic functions, it's time to learn some tricks that will come in handy as we graph different kinds of functions. Specifically, there are terms inside functions that do very predictable things to graphs, and if we learn what these are, we can look at certain functions and quickly graph them without making any tables, even functions that look super difficult. Who doesn't like a shortcut? Check this out!
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Ur a beast...much better at explaining this concept than my teacher.
Eric Moore any1 is better than my teacher, he doesn’t even try to teach he just hands us the notes and is like alright here is your homework and then does nothing for the rest of class
@@lastpot261 reason for that probably stems from public school teacher's confidence in their job security, but UA-camrs have to lecture well to attract more popularity? But in either way this UA-camr is really well at lecturing so I'd rather to spend time with him even though he charges in the future.
@@lawrenceliang6670hi
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!
Same.
I watch 10 per day.
@@Stoirelius you are not him
bro does not have the apple emojis@@ChefSporty
@@djpriest123 i have the iphone 42
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!
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!
Did u graduate yet
An absolute genius! He deserves an AWARD!
I can’t thank you enough for simple methods
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
So sad yet so true..................................
This is getting overwhelming right now
Can't remember this much of concepts.
Very clearly explained! A big thanks to you.
I can say that you and brian are really good at teaching, straight forward, you guys are the best
I have seen many videos about this subject. Your explanation is the best ever. Thanks
Thanks Professor Dave
I've been struggling to understand graphs all semester and you just explained it in 7 minutes, I actually love you
fr bruh
This was mighty helpful, thank you so much!
Thank you for this
Just one doubt
What is the difference between vertical and horizontal stretch?
Same doubt
I so love this! On my way to understanding things! Thank you!! 🤗
Another super great video!!! Thank you so much for creating these educational videos. They truly help. Thanks !!
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!
your videos are awesome, keep the good work bro
He is so much better than my Algebra teacher! Thanks for this lesson 🙂
Prof Dave , you are talented
Okay, can someone please explain the difference between the horizontal and vertical thingy for Dilation.
Awesome job professor Dave! Thanks
The whole video is summed up at 6:32
thanks
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.
Wow this was awesome!! All day I was struggling to understand and this was so simple and informative. Thank you’
VERY useful and clear!! many thanks;
i've never had problems with this concept but the way my teacher wants us to do it is so unreasonably complicated.
thanks a ton your vids help alot especially since ive been doing online school
This video was really informative...thank you!
what would the transformation be for square roots such as 3square root x
thank you
Bro you're here every time i need help bro... thank you so much
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.
ugh thank u for this!! i need to take a quiz & even with notes the whole concept was still confusing u cleared a lot of it up!
Not only super helpful but also has a kickass intro song. Wish I could give a super thumbs up
Nice video. It helped!
Thank you Professor
thank you so much for this, such a wholesome video to learn! God Bless!
Thank you.
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
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.
Thanks it helped a lot
SO GOOD!
the best teacher ever
You make it sound so easy as rare in a math teacher
Wow I'm speechless. 👏
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❤
The table is correct.
@@ProfessorDaveExplains Isn't it supposed to be opposite, where -h = shift right = positive?
Great work u man
so positive and negative are opposites and shrink means to get wider and stretch means to get more narrow
even after all this time this is video is very good
Link to the "other strategies later in the series"?
3:45 it's not a horizontal stretch but it's a horizontal shrink !!
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!
saw that too, i had to watch the video again
thanks
I only watch so that I hear the 'check comprehension' music.
It sounds better when it's sped up by 1.5.
Is it "horizontal compress" at 3:37 instead of "horizontal stretch" as you say? Please check it up.
a stretch can be applied in the positive or negative direction, either way we refer to it as stretch.
@@ProfessorDaveExplains it either compressed or stretched ?????
Thank you
Keep it up 🙂
I love it here.
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
Yes
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?
That's correct. Think of the minus sign in (x-h) being part of the original form (like a formula). If h is positive, you have (x-h). If h is negative, you have (x-(-h)), which becomes (x+h).
Beauty of math.....😍😍😍
Great video
👍👍 Which program did u use? Thanks
do you have a link to ths powerpoint that I can print out. Your are so helpFUL thanks a bunch.
it's not powerpoint it's a video
Oh so not printable. This was very useful thanks.
you are the best
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!
nice video
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!
This is what I though too
It's not a typo. It's because it says x - h. The sign is not included (if it was, it would say x + h). That means that a positive h, which is then inverted, produces a shift to the right. Hopefully that was clear.
@@ArthasFB Thank you for your explanation. However, I'm afraid I still don't understand because the formula on the table doesn't match the explanation Prof. Dave gives @2:27. I'd appreciate any further clarification. Thanks again!
@@elhadjitalla3054 The video says x + 2 generates a shift to the left. That is, x plus a positive number. The same way, x - 2 generates a shift to the right. That is, x plus a negative number (or minus a positive number).
You can express that as x + h where if h is positive, it shifts to the left and if h is negative, it shifts to the right. In the example, h is 2.
But it is easier to remember if h being positive generates a shift to the right. For that, we can flip the sign of h (x - h). This means if we plug a positive number in h, let's say 3, it gives x - 3 and so the shift is to the right. Notice that the sign is not part of h. For a negative value, - 3, it gives x - (-3) = x + 3 and so it is a shift to the left.
@@ArthasFB Wow! Thank you so much for your patience and kindness. I think I got it now! So it's all about the sign of the number you plug in for h. Thank you again so much!
is it inappropriate to call it 'horizontal compression', instead of stretch? or, is it requisite?
did you find out?
@@thubbard722 are you thomAs
@@mercilessanimations161 no haha
🥇
Shouldn't it střech horizontally too in the bottom example? It doesn't make sense to me :D 3:49
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"?
No, because the negative sign is not part of h, so a positive value for h is negated and produces a shift to the right.
How is it (-2)^3=8
actually the conditions for streches are not expressed correctly.
for example in 6:30 :
a>1 is fine but a
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 :>
are you try to input a value for x as (x+2)? writing it like that would mean the resulting function is (x+2)^2 , which expanded would be x^2 + 4x + 4 would have to convert to vertex form
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?
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?
note that subtracting a negative number gives you a positive number and vice versa
@@ProfessorDaveExplains Oh I see, thank you very much for quick response and awesome content!
Dheivame 🙇
The page at 6:33 shouldn’t positive h= shift left not shift right same with nagative h should be shift right
Don't forget that the h term is subtracted.
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?
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.
but don't forget that minus a negative h is positive
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!
You’re confusing the sign on the term with the sign already present in the binomial. The video is correct.
@@ProfessorDaveExplains YEAH YOU TELL EM DAVE. SPANK HIM LIKE THE NAUGHTY BOY HE IS AND PUT HIS ASS TO BED 😡 😩
Wish i could found your channel more earlier 😊.
Ur super sir... Love from Pakistan ❤❤❤
pakistan zindabad
My math teacher seduced me to watch this video
best intro
I have a test on this tomorrow and if I pass it’s not going to be thanks to my teacher, updating when I get my results
did you pass lol, its been over a year.
@@ambulantgaming8483 LMFAO yeah i think i did but i forgot to update 🧖🏻♀️
DAVE!!!!!!! I LOVE YOU SO MUCH DADDY!!! YOURE SHIFTING MY FUNCTION UP RIGHT NOW 😏😏
okk this is a good video very helpful for my exams the thing is at around 2:14 you said horizontal shit HHAHAHAHAH
wouldn't positve h shift left and the other vise versa 6:25
make sure to note that the term is subtracted
How -2 square = 4 can you explain
negative signs cancel when you multiply
But why it doesn’t show on calculator
it should. make sure you use parentheses.
Yeah now it shows
Thanks 🙏
Who else is here cause they're failing their algebra class? ;)
Nope, only you buddy
this is precalc not algebra buddy
@@jenniekim6649 no its algebra to I'm doing it in my algebra class
Me
Here because of legend Sir lodhi
Yup I'm here tooo
im getting carried by prof dave in all my subjects
Fucking god sent
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
the graphic is correct, don't forget to take into account the negative sign before the h term.
@@ProfessorDaveExplains sorry to be annoying but I think I am still confused, at 2:31 you said f(x)=(x+2) causes a shift left? but at 6:28 it says this causes a shift right ? thanks for your reply
So it's just that you're not considering the subtraction, if h is positive, then you subtract positive h and you get minus h. If h is negative, you subtract negative h and you get plus h. When I'm listing the sign of h, I'm not considering the subtraction sign.
@@ProfessorDaveExplains okay I understand now thanks for the help !
@@ProfessorDaveExplains Oh I get it, that is why you specifically noted (x-h), that is the positive h shifting right compared to (x-(-h)) being the negative h which would shift left. Correct?