Shifting, Stretching and Reflecting Parent Function Graphs
Learn how to recognize shifts, vertical and horizontal stretches and reflections as they affect parent functions in this free math video tutorial by Mario's Math Tutoring.
0:00 Intro
0:22 Diagrams of 6 Basic Parent Functions
1:07 Looking at a Horizontal Shift of the Square Root Function
1:53 Looking at a Horizontal Shift of the Absolute Value Function
2:15 Vertical Stretch of the Reciprocal Function
2:57 A General Way to Analyze Shifts, Stretches and Reflections
3:44 Example of Transforming a Cubic Function
4:00 A Shortcut for Graphing by Shifting the Origin or Starting Point
4:50 A Reflection of the Step Function
5:29 A Horizontal Compression of the Quadratic Function
6:23 More Challenging Example
8:18 A Simpler Way to Graph Taking the Translation into Account First
9:37 A Summary of the Transformations
10:26 A Reflection Over the x-axis
Related Videos:
Graphing Step Functions
• Graphing Step Functions
Graphing Square Root & Cube Root Functions
• Graph Square Root and ...
Graphing Parabolas in Vertex Form
• Graphing Parabolas in ...
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A random ad : "Are the videos from 2006 really helping you ?" Me : well , 2 + 2 is still gonna be 4 even after a thousand of years , so yeah these old videos are really helping me
@ButerWarrior44
2 жыл бұрын
ikr
watching this video two minutes before an exam.
@MariosMathTutoring
6 жыл бұрын
+Bender Bending Rodriguez report and let me know how you did!
@000zzx9
6 жыл бұрын
living on the edge
@bostonjackson9384
6 жыл бұрын
Seems like he didn't make it. He's gone.
@barta5ot-395
6 жыл бұрын
rip
@benjaminsanati7078
6 жыл бұрын
Seeing as he watched an 11 minute video in two minutes it doesn't look like everything went as planned
When Jeff Bezos can teach you math.
@IvanIvanov-zm1ot
2 жыл бұрын
That's fucked up dude. This is great free content, which helps many students succeed because their teachers are not good. Be appreciative, you are obviously here because you need help, so don't be a hater, show love and support to Mario for giving you this free and well put education. Stop being a smart ass and offending people for comment likes. Ever thought how your comment can make Mario feel? Grow up, and if you don't have anything nice to say, then don't say anything.
@sunacchi8240
2 жыл бұрын
@@IvanIvanov-zm1ot Bro what? I love Mario's stuff, he helped me a lot through precalculus lol. Your knees gotta be mad sore from jumping to so many conclusions. Your sense of humor is lacking and it shows 🥱
@lilylopez4373
2 жыл бұрын
@@IvanIvanov-zm1ot you really responded to a comment from 2 years ago. And it was an obvious joke 😭
@brazytales7916
2 жыл бұрын
@@lilylopez4373 😭😭🤣🤣
@lemon-vy3mj
2 жыл бұрын
@@IvanIvanov-zm1ot You really thought you saved the world by saying that? 🗿
I have a test on this content on Monday god bless you. My math teacher just kinda blew over this stuff and acted like we already all knew it
I was absent when my teacher taught this, the next class he just gave me the papers and didn't explain anything. Thank you! You helped me a lot, I hope I do good on my test tomorrow.
@MariosMathTutoring
5 жыл бұрын
Glad my video helped you! Good luck on your test! Report back if you want and let us all know how you did.
@geraldjinx
Жыл бұрын
did you pass
@nolanledwith2039
Жыл бұрын
What you get bro?
@suso5782
Жыл бұрын
@@nolanledwith2039 3 years later I'm reporting that I passed the test, passed the class and graduated High School 2 years ago! Hardest years of my life due to depression and all that but I made it!
@s1643
Жыл бұрын
@@suso5782 CONGRATULATIONS
Thank you so much. Hours of homework made no sense to me until I saw this video. Thank you, thank you
Videos like this remind me why some people have a job as a teacher. Thank you! Clear, to the point.
Thank you so much, when I get stummped I look for your videos and you are the most helpful out there!!!!
Mario, Thank you for being an excellent teacher when it comes to this. I learned faster from you than my instructor. Best.
@MariosMathTutoring
4 жыл бұрын
Glad my video helped you Ryan!
My teacher wasn't very good at explaining this.. you helped so muchhh thank youuu 👌
@MariosMathTutoring
6 жыл бұрын
+tylerposey iseverything your welcome! Glad my video helped you!
@michaelbrowne4525
3 жыл бұрын
I taught you well you just did not pay attention
@throwingfacts1132
3 жыл бұрын
@@michaelbrowne4525 Then why are you also here? need tips urself? 🤣
@michaelbrowne4525
3 жыл бұрын
@@throwingfacts1132 that was a joke I dont know anyone there... great video tho
@throwingfacts1132
3 жыл бұрын
@@michaelbrowne4525 I know, I went along with your joke lol
This was an absolutely fantastic explanation of basic graphs and functions! I'm taking pre calculus and this is all I need to know to understand most of the course. Thanks!
@MariosMathTutoring
4 жыл бұрын
You’re welcome!
this is really nice, kind of feels like being in a physical math class again, but with like a teacher who matches my needs pretty well already by default lol.
oh my goodness, this helped me so so much! thank you for creating, great explanation!!!
@MariosMathTutoring
6 жыл бұрын
+Jacey Wilson your welcome! Glad my video helped you!
Best quick and easy explanation! Thanks Mario!
This was super helpful!! I’m currently in pre ap pre cal and watching review vids like this are a big help
@MariosMathTutoring
4 жыл бұрын
Glad my video helped you!
This is such a helpful video! Thank you so much, I missed a lecture on this an was feeling stressed about it but now I get it!
@MariosMathTutoring
5 жыл бұрын
Glad my video helped you catch up on this topic Marcie!
Mario you are the best!!!You explain calme and with logic!!
@MariosMathTutoring
4 жыл бұрын
Thanks! Glad you like my explanations in the videos!
Thank you so much. I got stuck with a terrible math teacher this semester and your videos are helping a bunch.
@MariosMathTutoring
5 ай бұрын
Happy to help!
Thank you, this video helped me out alot in reading functions!
@MariosMathTutoring
4 жыл бұрын
You’re welcome! Glad my video helped you!
Good stuff. Short and informative.
I can't thank you enough for this easy to understand video.
@MariosMathTutoring
6 жыл бұрын
Your welcome! Glad my video helped you!
This was extremely helpful to me. Thanks a ton!
@MariosMathTutoring
6 жыл бұрын
Your welcome! Glad it helped!
Great video, clear explanation! Appreciate the help!!
@MariosMathTutoring
6 жыл бұрын
+Destiny Smith your welcome! Glad you liked the video!
Great videos, this explanation is way better then my math teachers. Please keep making much great videos
@MariosMathTutoring
5 жыл бұрын
Glad you like my videos Adarsh!
This video is helping me pretty nicely. I’m currently taking pre-Calc right now and this is the second time I’m taking it after failing it the first time
@MariosMathTutoring
4 жыл бұрын
Glad my video is helping you Collin! Lots of PreCalculus videos on my channel to help you get through this class.
thank u! i have a test tomorrow but i feel like i can ace it now!!
Thank you very much. I really needed the explanations.
@MariosMathTutoring
5 жыл бұрын
You’re welcome! Glad my explanation helped you!
This is really helpful!
@MariosMathTutoring
4 жыл бұрын
Glad my video helped you!
Great video. You taught so well !! 🤙🏿
@MariosMathTutoring
4 жыл бұрын
Glad you liked my video and my teaching method Renan!
Thanks so much. Here everything is super easy!😊
@MariosMathTutoring
4 жыл бұрын
Glad my video helped you Parvina!
Very well explained!
Hey. Loved the vid but I have a question. What do I do if their is no parentheses or radical or absolute value to help identify what’s on the outside or not. Please help
Thank you so much this helped a lot!
hey guys do the growth factor, the a, affects the k?? like do we times/multiply to it or do we just leave it?
This helped me a lot.
Thanks Mario for the great vid!
@MariosMathTutoring
6 жыл бұрын
+Floris Westerbeek your welcome!
Very helpful!!! Thank you so much!!!
@MariosMathTutoring
6 жыл бұрын
+Boston Jackson your welcome! Glad my video helped you!
This is a great video, Thanks for the help.
@MariosMathTutoring
6 жыл бұрын
+Hasan Mohammed your welcome...glad the video helped!
A very helpful video. Thank you very much :)
@MariosMathTutoring
6 жыл бұрын
Your welcome! Glad it helped you!
Thank you it was really helpful
Mario you are a lifesaver
@MariosMathTutoring
6 жыл бұрын
+Oskar Lange glad my video helped you!
On y=1/2 how do you shift units to the right or left?
Thank you so much!
you are an awesome math teacher. Thanks !
@MariosMathTutoring
6 жыл бұрын
Your welcome! Glad my videos are helping you!
@j5803
6 жыл бұрын
your profile pic looks like the absolute function
THANK YOU!
Do you have a vid explaning about g in terms of f? It is related to parent function .
Very helpful! God bless you
@MariosMathTutoring
5 жыл бұрын
Glad my video helped you Elizabeth!
this is great.... thank you
@MariosMathTutoring
6 жыл бұрын
Your welcome!
great video!
@MariosMathTutoring
6 жыл бұрын
+Monica Mejia glad you liked it!
This is helpful! thank you!
@MariosMathTutoring
6 жыл бұрын
+Hope Xiong your welcome! Glad my videos are helping you!
Want to learn how to do more challenging transformations? Be sure to watch the video I did here: kzread.info/dash/bejne/ppWYt9ymn5jKpbg.html
watching this right before my algebra 2 midterm. wish me luck
Awesome!!! Thanks so much!
@MariosMathTutoring
6 жыл бұрын
+Gordon Felesina your welcome. Glad my video helped you...
I understand the concept of the "step function", but it definitely can get a little tricky when dealing with transformations!
@MariosMathTutoring
6 жыл бұрын
+Chris Manhoff here is another video I did on step functions that may help you kzread.info/dash/bejne/pnyr0sxykpfgitI.html
l have my math final tomorrow... this helped me so much! Thanks!
@MariosMathTutoring
6 жыл бұрын
Great! I’m glad my video was able to help you!
@timemachinestudios8413
6 жыл бұрын
me 2, fuck
THANK YOU MARIO! I was doing deltamath and it did not teach me the meanings of the transformations!
@MariosMathTutoring
6 жыл бұрын
You’re welcome Jolie!
Also would g (x) = (x-1)^ -5 be horizontal translation right 1 unit and vertical translation down 5 units
@jt6170
5 жыл бұрын
Yes
thank you so much
Very well done!
@MariosMathTutoring
3 жыл бұрын
Glad you liked the video!
Dear Mario, In case of 1/x function, the graph of 2/x is vertically shrunk instead of stretched as it is more away from y axis as compared to 1/x graph. What is your opinion? Regards. In fact 1/x and 1/x^2 have shrinking/stretching about origin.
@MariosMathTutoring
6 жыл бұрын
Very thoughtful questions. As far as shrinking and stretching...2/x is a vertical stretch from the parent graph 1/x meaning it is being stretched such that it is further from the x axis so to speak. As far as 1/x and 1/(x^2) these are 2 different functions...if you compared 2/(x^2) to 1/(x^2) it would be a vertical stretch. Hope that helps you!
Anyone else feel the chills when that marker hits the board?
Dear Mario, How would u write an equation of a 1/x function with a vertical compress. Would it be 1/2/x for example or??
@MariosMathTutoring
5 жыл бұрын
Yes I believe you got it....or you could write it as (1/2)(1/x)....but not 1/(2x) because the way that one is written points more to a horizontal compression by 1/2. Hope that helps!
Thanks
Thanks I finally understood
@MariosMathTutoring
5 жыл бұрын
Glad my video helped you!
thank you
Thank you saitama for teaching us how to defeat the evil villain
this is amazing
@MariosMathTutoring
6 жыл бұрын
Glad you like the video!
Really good teacher
@MariosMathTutoring
6 жыл бұрын
Thanks!
how do you express the shifts made for this function >> f(x)=|2x-1|
Thank you so much
@MariosMathTutoring
4 ай бұрын
You're most welcome!
Yo this was so useful thx
@MariosMathTutoring
5 жыл бұрын
You’re welcome!
thx this helped allot
@MariosMathTutoring
4 жыл бұрын
You’re welcome Sharv!
Thank you sooo much
@MariosMathTutoring
5 жыл бұрын
You’re welcome Samantha!
thank you so much!!
@MariosMathTutoring
6 жыл бұрын
Your welcome!
life saver
Also for -2 (x+3)^ + 4 when your graphing a parent function would u move all your original points to the left 3 units and up 4 units
@MariosMathTutoring
6 жыл бұрын
+Matthew Joseph yes that is correct.
@matthewjoseph236
6 жыл бұрын
The a value would be -2 so wouldn’t it be vertical compression by a factor of -2
@MariosMathTutoring
6 жыл бұрын
+Matthew Joseph The negative reflection over the x-axis and the two stretches it
Would the description of the transformation g (x) = -2 (x+3)^ + 4 be reflection across the x axis vertical compression by a factor of -2 horizontal translation left 3 units and vertical translation up 4 units
@MariosMathTutoring
6 жыл бұрын
+Matthew Joseph it would be a shift left 3, vertical stretch by 3, reflection over the x axis, then shift up 4. Remember if the ‘a’ value is greater than 1 it is a vertical stretch and if it is between 0 and 1 it is a vertical shrink(compress). Great questions.
@LethalTalentz
6 жыл бұрын
Mario's Math Tutoring stretch by -2
Thank sir!
@MariosMathTutoring
5 жыл бұрын
You’re welcome Wajahat!
Thanks a lot teacher :)
@MariosMathTutoring
4 жыл бұрын
You’re welcome!
you look ethereal!!!
Thanks great video. You gained another subscriber Kudos from a later in life mathlete . And remember don't drink and derive! [hope you got the Calculus I silly joke].
@MariosMathTutoring
6 жыл бұрын
Glad you liked the video David! Welcome to the channel.
God bless you
@MariosMathTutoring
5 жыл бұрын
Glad you liked the video!
how to identify from given equation of function ,if it is one one ,many one etc
CLUTCHHH!!
@MariosMathTutoring
3 жыл бұрын
Glad my video helped you Yousef!
I dint really get half of this but thanks
The class was awesome but slightly increase font size 😊😊
wait for the square root of x + 2 problem why did we subtract 2 if there is a plus sign
2 classes away from a quiz that imma fail. But maybe not after this 😂
@MariosMathTutoring
4 жыл бұрын
Glad my video helped you Wren! Good luck on your quiz!
That is good , thx
@MariosMathTutoring
6 жыл бұрын
+Fresh M. Your welcome
U make it easier for me
@MariosMathTutoring
5 жыл бұрын
You’re welcome!
Heello! First of all I would like to thank you a lot for this useful video or lesson that I cannot understant yesterday in class because our teacher used to go so fast! I understand it now! But, I don't know what does it mean the fifth function! y=[x] this is the first time I see it! Please may you answer to my question, teacher? Thank you!
@MariosMathTutoring
5 жыл бұрын
Glad you liked my video Fatima! That is the greatest integer function which is sometimes referred to as a step function because the graph looks like stairs...
@fatimaben-akhmeij4890
5 жыл бұрын
@@MariosMathTutoring Ah ok thank you so much! I am trying to draw the graph of y= x^2 -3x-4
@MariosMathTutoring
5 жыл бұрын
This other video I did on parabolas may be of use to you... Parabolas Easily Graph All Types kzread.info/dash/bejne/imFqtrl_iJa0d6g.html
why does x-2 shift to the right? if x is 1, then it'd be -2 and go in the negative direction. i'm confused.
Bless❄️💯
Sir ,can you pls tell why when we have a negative sign in the function, why the graph is shifted to the right???
@MariosMathTutoring
4 жыл бұрын
My Secret Math Tutor did a nice job explaining it in this video...go check it out: kzread.info/dash/bejne/oKNpm62DmNHKlsY.html
@eehub6710
4 жыл бұрын
@@MariosMathTutoring than you very much for this sir😊🙏
Preparing for SAT😞😞
Thx
@MariosMathTutoring
5 жыл бұрын
You’re welcome!
Subscribed
@MariosMathTutoring
5 жыл бұрын
Welcome to the channel Danny!
Me: Maths without letters. Not me: Maths with letters.
Im still a bit confused, what would the transformation be for f( x/5) and -f(x).
@MariosMathTutoring
5 жыл бұрын
f(x/5) is a horizontal stretch by 5....meaning the x values will be multiplied by 5. -f(x) will multiply the y values by negative 1 thus reflecting the graph over the x-axis....hope that helps!
@Samir-rd8xp
5 жыл бұрын
@@MariosMathTutoring thank you for replying so quickly, it does help. One more question, what if there is a fraction before f(x)? for example: 1/2 f(x)