Horizontal and Vertical Graph Transformations
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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 Transformations - 9 full examples as well as the basic outline of doing horizontal and vertical translations of graphs are shown! The audio is not the best, so sorry for that!!!!
For more free math videos, check out PatrickJMT.com
There are many videos there that are NOT on UA-cam!!
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thanks for the kind words.
i taught for a bit, but then gave up on it.
now i teach anyone bored enough on youtube to watch
dude buy a new mic. Amazing tutorial btw
Published in 2008
he is so clear.... its incredible...
i would really want this guy to be my teacher... but then again, i don't really want to review this anymore XD
who's got the skillz?! : )
uploaded 2008, the audio and laggy video is excusable
Preach it!
@bluishgirL08 no graphs are taught early on, so you should be seeing them in high school (and even middle school)
Thank you greatly! I've learned more from you in 20 minutes of videos than I have in class.
not sure what you mean about the tables
well, descartes and fermat probably both discovered the idea of relating algebra and geometry through graphing at about the same time. i am sure they probably noticed the shifts as early as anyone! creating the XY axis was the brilliance; after that, any observant math person could notice the graph shift stuff!
@McBirdec yea, on some of my early videos, that audio was not the best. i think i have fixed that though on anything that is not over a couple of years old.
For rational functions (a polynomial divided by a polynomial) you always have a vertical asymptote for any value of x that makes the denominator zero BUT AT THE SAME TIME does not make the numerator equal to zero. Since x = 0 does this, we have a vertical asymptote at x = 0 (that is, the Y-Axis).
Likewise, if we were given
f(x) = (x-2 )/ (x^2-4), there is only a vertical asymptote at x = -2
East or West Patrick is the best. You are the best. Please upload more videos so that the students who cannot go to coaching can do well.
I don't understand why if it is positive it moves to the left and if it is negative it moves to the right.
no problem!
Good God, does nobody ever explain WHY the graphs shift in the opposite direction??
hahah! now I am your math teacher!
good luck on the test! : )
ha, nice!
Thanks again patrick! I'm taking my class class for CALCULUS... and these videos are such a great help and reminder of graphing and finding areas of cylinders and disks!!! Recmmended you to like 3 different people in my calc class to watch your videos for MORE views ( & DONATIONS :) )
@MikayybeBabyy my pleasure! i am always here... : )
The way you explain each and everything is simply amazing!!!
Great job on your videos!!!!! :)
God bless you infinitely for these videos you put up. Thank you.
no problem, glad to help
i AM your math teacher! : )
Thank you so much! My teacher doesn't know how to teach and when I got for extra help she explains nothing
cassie SAME I HATE HIGHSCHOOL
+it's kyrah I'm learning this in middle school
+ItzStephie Games 8th grade?
+Alex Cuellar yes
thanks :)
Patrick! You don't know how well you've helped me on this. I had been staring at my textbook for sometime without figuring out how to work this out. You just helped me out!!! I love you!
Glad I could help you out :) come back any time!
The way I think about horizontal transformations: If I add something like 2 to x, y will get any value two units earlier than when 2 was not added, the graph shifts to left. If I subtract something from x, y will get any value 2 units late than when x was not subtracted, the graph shifts to right.
i think u forgot to add the -4 at the last part for the original
i look for help on youtube....yesterday I needed help...and your video saved me..then I look for help today...and I see this video and Im like this is good...then I see the person who did this and it was your channel AGAIN!!! THANKS MAN!!! ^^
Good vid! To make this concept more intuitive (why F(x+k) is on the left of the graph) I usually try to explain that it can be thought of in time, so x = t. If you add k to t, you are making it occur earlier in time than f(t). Earlier in time is to the left on the graph. Now imagine you don't start you experiment until t=0. So from that reference, it makes the +k show up on the left hand side of the origin on t. It's all relative to your reference frame. It's more of a signals view of it. This can be compared to an oscilloscope screen. The (x+k) will make the event occur a k seconds earlier then f(x). This will push it to the left of the o'scope screen.
God I love you
This is easy stuff though compared to trigonometric and integral eqations ;) i have those at my university.
Anyway, good job.
OK it seems to be pretty simple but what is the purpose of shifting a function, where do we get this kind of situation? I mean what kind of problem would ask this transformation? If you see what I mean.
This helped me so much. I finally get why we take the number that manipulates the x in the context of (x-1) and take it as (x+1). I just wasn't getting it before.
thank you so much!!!
hey patrick thanks man, could you do a video of shifts in terms of x
i mean for example x=y^3
now how do the shifts work ?
thanks by the way
I really wish methods of teaching mathematics would catch up to modern mathematics. A few examples:
-Stop teaching x as a sign for multiplication. Simply use the center dot or grouping symbols ( ).
-Similarly, stop teaching the ÷ symbol. Represent it as a fraction. I'd even hesitate to use the / symbol, since that means something different in higher mathematics.
-Start teaching functions earlier. f(x), g(x), h(x), etc.
There are many others, but they are outdated.
Thanks for the vid, btw.
hehe, such as me? :), seriously man, thanks, I mean more than that, I got these 2 questions right cause of the help I got from this video and another video which I also commented on (completing the square), btw does youtube pay you?, if they don't, then should :)
Thanks for the Video!
Helped clear up some things. 5/5
I could really do with a hand to understand this as well. I don;t like just rote learning a rule - to understand WHY would be really helpful !
Great video series - I couldn't get by without them.
I love you. Point. Blank. Period. I can't believe how easy you made this stuff seem in less than one hour. 0__0
you helped me understand this in minutes vs. reading through pages of babble. Thanks a ton, I'll be checking out some of your other videos as well, I'm sure. Cheers!
dude you are amazing.. because of you im gonna be at least writing something on my exam paper!
YOU ROCK
What helped me to understand the reason y =(x + 2)^2 shifts left and y = (x - 2)^2 shifts right was realizing that the parent function y = x^2 has it's vertex at the origin, (0,0), The x-intercept occurs when y = 0, so 0 is the x-intercept.
For y = (x + 2)^2, y = 0 when x = -2, so the x-intercept is -2 and the vertex is at (-2, 0), which is shifted 2 units to the left of the origin.
For y = (x - 2)^2, y = 0 when x = 2, so the x-intercept is 2 and the vertex is at (2, 0), which is shifted 2 units to the right of the origin.
thanks this explanation is very clear and simple to understand.
Good luck on me! Just started Summer quarter, and I can already sense my instructor is just horrible to say the least. :-/
so lucid explanation ....with voice clarity hoping a little better next time
but overall a lot of thanks as it helped me a lot.Thank you sir
my textbook was wrong... it said if k>0 it moves right and if k
Good video. Sometime it is easier to draw the graph by shifting the y-axis and x-axis instead of redraw the graph..
@YJ4 thats simple just set it to 0, for example x-1=0 and then solve the equations, which equals x=1. got it bud?
very helpful thanxxx
but if u would have drawn that last graph also than it would have cleared my doubt
Yeah, the audio on this is almost unbearable. The effort is awesome and much appreciated.
i love you man! these videos are amazing! you're better than my actual algebra 2 teacher!
awesome. sound quality's not as good as the floor function video but still a great video
If my high school teacher was more like you I would have no problems with math today :)
thanks for helping.
know i can solve Horizontal and Vertical Graph Transformations.
thank u. youve explained better than my college prof cuz he's been confusing me.
Wait how can that be that would mean that x at one point would be 0 and you can't divide my 0. I don't get it
how do you find the exact numbers of the points for the base functions?
Thanks for all your videos they have helped me through algebra
"My artistry isn't the best" ... saying that as his work looks great lol
Maths exam in two days. Life is much easier now. Thank you kind Sir.
I second that, this guy is amazing, btw, patrick, do you teach class?
i found this 12 years later.... whatt still helpful
nice :) but how do you graph roots, i have a question y = 2 root x
good vid ! where did you learn this math ? college ? high school ?
Thank you! Thank you! Thank you!
At a glance, I thought that said something other than praise....
that was the best explanation of transformations of graphs
thank you so much, u explain this way better than my teacher
you're left handed!!!!]
tnx definatley a good teacher :)
I have watched all your videos. Thanks so much Patrick
Ah phew! thank you it' morning before my maths exam aha
Thanks for the videos. I like to rewrite y = 1/x + 2 using a common denominator:
y = 1/x + 2
y = 1/x + (2x)/x
y = (1 + 2x)/x
Now I can see that the horizontal asymptote is y = 2/1 (coefficient of x's - both with degree 1), which is y = 2.
great video just need a new microphome
oops, i don't know what i was thinking
seriously man .. you rock .. thank you so much .. :)
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Patrick's videos? YES.
When you originally posted this I was four and now I'm taking calculus oh how the times have changed.
i know! i've gotten fatter and have much more grey hair
What kind of a teacher chews on their sharpie?! xD
Youre much better then my stupid precalc teacher
but i thought it is the axis that moves and not the function
you-are-the-best
Great information but the audio on this video is horrible is sounds very scratchy, I thought it my be my computer speakers so I tried my Bose headset and it is definitely the video is horrible audio quality
good one,,,I really leart from this
realy shiet audio quality and video framrate is shiet as hell made in 2008 iknow...
but the teaching quality is incredible
@YJ4 YEAAAH it just messes every thing up.
thank you for explaining everything the math instructors i have had in college could not explain this to where i could grasp the idea in its entirety
Very exhaustive, good approach
lefty you are jmt
ok so What makes the graph upside down
video quality = 10/10
thanks, it was a lot of help! cheers.
thank you so very much. it really helped me understand transformations better.
Thank you, it seems much esier than what i read in my revision guide!
I LOVE THAT I'M 725 ON THE LIKES.
I got my IB exams tomorrow and this really just cleared my doubts, thank you so much! Your videos are really helpful and its a wonderful thing you're doing! :)
Very helpful. I was looking for this exact concept, thank you!
What's the next video after this?
This helped so much!! If only the math teachers at my school were good at teaching math like you. Thank you!
2-x same as -x+2 ?
Yes
Thank you this makes sense now.
I guess yes