Horizontal And Vertical Graph Stretches and Compressions Part 2 of 3
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- Опубліковано 1 жов 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Horizontal And Vertical Graph Stretches and Compressions Part 2 of 3. In this video I discuss horizontal stretching and compressing of graphs.
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"I'm not a great artist" - All math teachers
Thank you! :)
yes, that is what basically happens.
if you see f (cx), you can basically multiply each x-coordinate on the original graph by 1/c, leave the y-coordinate alone, and that will give you a new point on the 'transformed' graph
well, the 'intuitive' idea is that since you are halving the inputs (that is, you are picking an x coordinate, and dividing by 2), so to get to the same 'original x value' (and so the corresponding y-coordinate) you would have to go out twice as far, thus stretching the graph horizontally by a factor of 2.
i recommend graphing y = (x ) ^ 2
and also y = ( 2x ) ^ 2 by plotting points to see this idea!!
yes, y coords change during vertical stretch / shrink ; x coords change during horizontal stretch / shrink
Not understanding why you divide x-coordinate by 2 when it's y = f(2x)
@MintedCoin that is a good question... i actually do not think i made it
where is part 3 I really need it.....
+karnvir bhangu the part 3 is just reflecting along the y-axis and x-axis
perhaps YOU should think about why this stuff happens. it is not that deep but does require a bit of thought....
well , i think this is some ambiguity in the english language. do you cut something in half or in 2?
@TazMania757 no, no i am not
correction... for the graph y=f(2x) u are not multiplying by the x-values, u are dividing by them..example (-4,1) ur new point would be (-2,1)...
@Romania007 well, that is a pretty vague question. my answer would be: no
So that's what it meant by "factor of 2"! I've found that the part I love most about studying math is the a-ha! moments, and you just gave me one, and I know you'll give me plenty more. Keep up the awesome work! You're helping so many people to not drop out of college:)
ops! thanks for pointing out the mistake. glad it was ok otherwise!
@rodrainbow6 that is a good question
no need to be an a-hole there, champ.
@RyanxTran glad to be able to help!
@pktwin0w1 to each, their own!
ok 2x isnt cutting anything in half...iam confused
Thank yo so much for this video, I have been hammering my head to the wall all day trying to understand why if you are multiplying the input, the input that is actually used is the opposite of what you get on paper. For EX, if f(2x) and your input is 4, then logic tells me the input should now be 8, but in reality it's supposed to be 2. It the process still does not make sense to me, but for now one, if I see a whole integer like 2 or 4 etc..and its multiplied with the input, I'm just going to consider it as if I'm multiplying with a fraction. instead of 2 or 4, I will multiply by 1/2 or 1/4. ...ugh math
@klodya3 thanks! : )
I cant find part 3 for anything was it deleted?
*fireworks exploding in brain*
Probably because I had to drop out of high school in the ninth grade to work and take care or my paralyzed mother after my father died of cancer. It's a lot of work for me to understand all this, but thanks to Patrick I aced my College Algebra class:) Now I'm looking forward to calculus!
glad i could help :)
Thank you so much!!! You have the best way of teaching this stuff. All your videos have helped me. You are appreciated by me and my classmates!
I still don’t understand...
My only complaint about this video is how you define your horizontal compression/stretchs.
f(cx) is a horizontal compression by 1/c and f(1/c) is a horizontal stretch by c
When he says f(2x) that means a horizontal compression by 1/2
When he says f(1/2x) that means a horizontal stretch by 2
Stretches are always BY a number bigger than 1. Compression are always BY a number between 0 and 1
not everyone does this type of mathematics in high school. You are fortunate to be among those who have that opportunity, so take advantage of it in a positive way that doesn't belittle others who are obviously trying to learn or else they would probably watching something else. PatrickJMT rules!
Why do you cut the values in half even when you are multiplying the x value by two??? Your explanation made no sense
please explain if we by 2x for each value of x
so how is (-2,0) equal -1? in X ?
it should be -4
cz 2*-2=-4
i wait your answer
well, he didn't really mentioned it but what you do when you do y=f(2x) what you're doing is basically multiplying the x-coordinates by 2's reciprocal. so the reciprocal of 2 is 1/2 that is why he says the graph is compressing because you are multiplying by its reciprocal. Vice versa with y=f(1/2x). you are just multiplying all x-coordinates by the reciprocal of 1/2 which is 2.
so for y=f(1/2*x) you basically take an x intercept and multiply by 2???? why multiply instead of divide?
does it means that in vertical stretch/shrink, the y coordinates are e factor that change? while for horizontal stretch/shrink, x coordinates are e one changing?
@MintedCoin Just type " Graph Transformations about the X-axis and Y-axis" into youtube search bar. He made the vid, he just named it differently :)
So can you think about it as dividing the x coordinate by the factor?
X coordinate of -4 divided by 2 = -2(the new x coordinate in your first example)
This video was made the year I was born and I can't express how relieved I am to finally understand this topic after many UA-cam videos 😭
LOL i'm doing this math in Grade 11. How can you find this difficult in COLLEGE?!?!
Hey Patrick, thank you so much for all of your videos, you make math so easy to understand and fun to do... I was just wondering if you have part 3 of this video (Horizontal And Vertical Graph Stretches and Compressions )...
Thank you
@94Jaklin The blank circle means the function doesnt touch or include that point. It's called a jump discontinuity.
I like this video.. It shortened my learning curve but where is the part 3??
Or you could say for horizontal stretches and compression's you divide.
amazing explaination!
when you its (2x), shouldn't it be compressing it by a factor of 1/2
@klodya3 What is the different between F(halfX) and halfF(X)?
This really helped mee alot!
Just saying. I guess the curriculum is different where I live (Canada). And by the way, you've helped me a lot throughout high school ;)
thank u
Hi! Your videos are great - I'm learning a ton :)
Question to your y= f(1/2x) ex., how would you graph a function like, y= f(1/x+3) ??? In the above ex. you multiply 2 by the x coordinate. But in this function there is no value given for 'x' - y= f(1/x+3)
OMGG YOU ARE THE BEST!!! This really helped me it was exactly what i needed for my math assignment and now i am DONE well almost still need to watch the 3 video :P but yeaaa u are a great help keep posting videosss!!!@@@### =P
So are you saying that if you have a number that is greater than 1 inside the parenthesis, you can take that number and simply put a 1 over it? Would that make sense?
good stuff
K is the same is as scale factor, right?
makes the whole thing so much clearer! test tomorrow on this -- might have a chance now :P
thanks so much!
can someone tell me in simple terms what you would do if "a" is a fraction( for example divide it by the y values, ) and if K is a fraction? I already know that they're both compressions and I know that k is horizontal and a is vertical but I don't understand if your suppose to multiply whatever it is, plz help?
Love the videos.... I caught one little mistake; at 5:25 you say "the x value is going to stay the same" you meant to say "the y value is going to stay the same."
KEEP UP THE GREAT WORK! These help me a TON!
We were taught to take the reciprocal of the 'c' value, in the formula we use we call it 'b' but anyway so if the 'c' value is 3 the factor would be the reciprocal or 1/3... Is that what your saying
omg.. this concept is soo simple... my math teacher did not teach anything about it and there was nothing in the textbook that helped me out either. Thank you.. btw, wheres part 3?
thanks you so much for your videos! I'm taking college algebra online and my textbook sucks totally! I can get it only thanks to your great explanations ! Big Thanks :))
so you're not multiplying the x coordinate by 2 you essentially divide it by 2 or just halving it?
@ zachary williams This is how u do it.
2x=what ever the x value is.
solve for x. That's when u divide by 2.
Dude.... Thank you.
thanxs a lOt! :)
Pat, you are better than my college professor @ teaching. Good stuff.
when it is*
Vertical stretch/shrink = a * Y
Horizontal stretch/shrink = X / a
I really appreciate you for this video and Part 1. These 2 videos have helped me a lot to grasp the topic.
Thank you very much Patrick
This is an awesome tutorial! This helped out with a project. I was really unsure about vertical and horizontal compressions and expansions.
P.s-my math teacher always says he's not a great artist when he graphs also lol
At least he is capable of explaining these things.
but why they should stretch or verse i still didnt understand it.
you.fuckin.rule.
This helped so much. I've learned more in parts 1 and 2 than I have in my 4 1/2 months with my math teacher.
it got squished by a factor of 1/2 *****
You sir, are a scholar and a gentlemen.
Ahhh thanks! This helps for my test tonight!
LOL im doing this math in 8th grade.
Thank you soooo much!!!!
@patric
You are my man
THANK YOU SO MUCH!!!!!
very clear!
y=f(1/2x)-4
+james ricky it stretches the graph horizontally by a factor of 2 and shifts it downward by a factor of 4 :)
LOL i'm doing this math in Grade 9. (2 years ahead)