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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[@MariosMathTutoring]

mariosmathtutoring.teachable.com/p/learn-algebra-1-video-course Check out my Learn Algebra 1 Video Course for sale. I teach you chapter by chapter and section by section. There are 87 video lessons and over 11 hours of video. For less than the price of a private tutoring session you have lifetime access to the course and can work through it at your own pace. Check out the 13 free lessons (1 from each chapter) at the link above. - Mario

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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]

ikr

[@sunacchi8240]

When Jeff Bezos can teach you math.

[@IvanIvanov-zm1ot]

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]

@@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]

@@IvanIvanov-zm1ot you really responded to a comment from 2 years ago. And it was an obvious joke 😭

[@brazytales7916]

@@lilylopez4373 😭😭🤣🤣

[@lemon-vy3mj]

@@IvanIvanov-zm1ot You really thought you saved the world by saying that? 🗿

[@benderbendingrofriguez3300]

watching this video two minutes before an exam.

[@MariosMathTutoring]

+Bender Bending Rodriguez report and let me know how you did!

[@000zzx9]

living on the edge

[@bostonjackson9384]

Seems like he didn't make it. He's gone.

[@barta5ot-395]

rip

[@benjaminsanati7078]

Seeing as he watched an 11 minute video in two minutes it doesn't look like everything went as planned

[@AJ-Bunny-]

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

[@suso5782]

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]

Glad my video helped you! Good luck on your test! Report back if you want and let us all know how you did.

[@geraldjinx]

did you pass

[@nolanledwith2039]

What you get bro?

[@suso5782]

@@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]

@@suso5782 CONGRATULATIONS

[@Jenauxn]

Thank you so much. Hours of homework made no sense to me until I saw this video. Thank you, thank you

[@anobelkhoushabeh3831]

Videos like this remind me why some people have a job as a teacher. Thank you! Clear, to the point.

[@MrSupernova111]

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]

You’re welcome!

[@whitneycammack3056]

Thank you so much, when I get stummped I look for your videos and you are the most helpful out there!!!!

[@jaceywilson2182]

oh my goodness, this helped me so so much! thank you for creating, great explanation!!!

[@MariosMathTutoring]

+Jacey Wilson your welcome! Glad my video helped you!

[@ryanbates4570]

Mario, Thank you for being an excellent teacher when it comes to this. I learned faster from you than my instructor. Best.

[@MariosMathTutoring]

Glad my video helped you Ryan!

[@throwingfacts1132]

My teacher wasn't very good at explaining this.. you helped so muchhh thank youuu 👌

[@MariosMathTutoring]

+tylerposey iseverything your welcome! Glad my video helped you!

[@michaelbrowne4525]

I taught you well you just did not pay attention

[@throwingfacts1132]

@@michaelbrowne4525 Then why are you also here? need tips urself? 🤣

[@michaelbrowne4525]

@@throwingfacts1132 that was a joke I dont know anyone there... great video tho

[@throwingfacts1132]

@@michaelbrowne4525 I know, I went along with your joke lol

[@asterroux1102]

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.

[@fortimusprime]

Best quick and easy explanation! Thanks Mario!

[@marciebonet2232]

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]

Glad my video helped you catch up on this topic Marcie!

[@MariosMathTutoring]

Want to learn how to do more challenging transformations? Be sure to watch the video I did here: kzbin.info/www/bejne/qpLHhq2jpJqXq7c

[@valeriaguerrero7152]

This was super helpful!! I’m currently in pre ap pre cal and watching review vids like this are a big help

[@MariosMathTutoring]

Glad my video helped you!

[@marijetaromicilic8548]

Mario you are the best!!!You explain calme and with logic!!

[@MariosMathTutoring]

Thanks! Glad you like my explanations in the videos!

[@zboyzz1827]

Thank you so much. I got stuck with a terrible math teacher this semester and your videos are helping a bunch.

[@MariosMathTutoring]

Happy to help!

[@collins3919]

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]

Glad my video is helping you Collin! Lots of PreCalculus videos on my channel to help you get through this class.

[@lineitempoliticheads6100]

Thank you, this video helped me out alot in reading functions!

[@MariosMathTutoring]

You’re welcome! Glad my video helped you!

[@NicoleCorby]

I can't thank you enough for this easy to understand video.

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@Khaloood125]

Good stuff. Short and informative.

[@arjundas7078]

This helped me a lot.

[@mishtirelan3637]

This was extremely helpful to me. Thanks a ton!

[@MariosMathTutoring]

Your welcome! Glad it helped!

[@taruva]

thank u! i have a test tomorrow but i feel like i can ace it now!!

[@destinysmith3497]

Great video, clear explanation! Appreciate the help!!

[@MariosMathTutoring]

+Destiny Smith your welcome! Glad you liked the video!

[@fouziasiddique6536]

Very well explained!

[@twinflameslime]

Thank you so much this helped a lot!

[@lagoonaa2003]

This is really helpful!

[@MariosMathTutoring]

Glad my video helped you!

[@sha1na]

THANK YOU!

[@obscenecaffeine9876]

Thank you so much!

[@tuanpham8093]

hey guys do the growth factor, the a, affects the k?? like do we times/multiply to it or do we just leave it?

[@aabattery4092]

Thank you very much. I really needed the explanations.

[@MariosMathTutoring]

You’re welcome! Glad my explanation helped you!

[@kelvinmabvurudza4941]

Thank you it was really helpful

[@AbdulAziz-qp2iq]

this is great.... thank you

[@MariosMathTutoring]

Your welcome!

[@floriswesterbeek9675]

Thanks Mario for the great vid!

[@MariosMathTutoring]

+Floris Westerbeek your welcome!

[@bostonjackson9384]

Very helpful!!! Thank you so much!!!

[@MariosMathTutoring]

+Boston Jackson your welcome! Glad my video helped you!

[@adarshpettappa7583]

Great videos, this explanation is way better then my math teachers. Please keep making much great videos

[@MariosMathTutoring]

Glad you like my videos Adarsh!

[@juanparra6796]

On y=1/2 how do you shift units to the right or left?

[@parvinajamshidovna7487]

Thanks so much. Here everything is super easy!😊

[@MariosMathTutoring]

Glad my video helped you Parvina!

[@renan6827]

Great video. You taught so well !! 🤙🏿

[@MariosMathTutoring]

Glad you liked my video and my teaching method Renan!

[@lol-pf9cq]

thank you so much

[@renewd]

I understand the concept of the "step function", but it definitely can get a little tricky when dealing with transformations!

[@MariosMathTutoring]

+Chris Manhoff here is another video I did on step functions that may help you kzbin.info/www/bejne/qnnaoZ1vl5mtkNE

[@Hasan_1301]

This is a great video, Thanks for the help.

[@MariosMathTutoring]

+Hasan Mohammed your welcome...glad the video helped!

[@oskarlange7557]

Mario you are a lifesaver

[@MariosMathTutoring]

+Oskar Lange glad my video helped you!

[@jannrubena.tolentino8205]

Do you have a vid explaning about g in terms of f? It is related to parent function .

[@monicamejia3124]

great video!

[@MariosMathTutoring]

+Monica Mejia glad you liked it!

[@hopexiong8582]

This is helpful! thank you!

[@MariosMathTutoring]

+Hope Xiong your welcome! Glad my videos are helping you!

[@gordonfelesina8146]

Awesome!!! Thanks so much!

[@MariosMathTutoring]

+Gordon Felesina your welcome. Glad my video helped you...

[@nourzakaria6862]

A very helpful video. Thank you very much :)

[@MariosMathTutoring]

Your welcome! Glad it helped you!

[@maxgoldstein1536]

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

[@ElizabethHernandez-fw3zi]

Very helpful! God bless you

[@MariosMathTutoring]

Glad my video helped you Elizabeth!

[@aids1580]

This was so so helpful thank you. About to take a quiz today wish me luck.

[@MariosMathTutoring]

You can do it!

[@matthewjoseph236]

Also would g (x) = (x-1)^ -5 be horizontal translation right 1 unit and vertical translation down 5 units

[@jt6170]

Yes

[@laceybrooks9244]

thank you

[@The_S_S_]

thx this helped allot

[@MariosMathTutoring]

You’re welcome Sharv!

[@shuminchen815]

you are an awesome math teacher. Thanks !

[@MariosMathTutoring]

Your welcome! Glad my videos are helping you!

[@j5803]

your profile pic looks like the absolute function

[@fazalmian3701]

this is amazing

[@MariosMathTutoring]

Glad you like the video!

[@yashkhurana9170]

thank you so much!!

[@MariosMathTutoring]

Your welcome!

[@arwaali9390]

Thank you so much

[@MariosMathTutoring]

You're most welcome!

[@samanthacherubin9911]

Thank you sooo much

[@MariosMathTutoring]

You’re welcome Samantha!

[@j5803]

THANK YOU MARIO! I was doing deltamath and it did not teach me the meanings of the transformations!

[@MariosMathTutoring]

You’re welcome Jolie!

[@joeblow1688]

Very well done!

[@MariosMathTutoring]

Glad you liked the video!

[@user-rl7ni4rc9m]

Thanks

[@edalbyek6060]

Yo this was so useful thx

[@MariosMathTutoring]

You’re welcome!

[@lanjalanja733]

how do you express the shifts made for this function >> ‌ f(x)=|2x-1|

[@pradyumnvashishtha983]

life saver

[@carolinebowen5140]

l have my math final tomorrow... this helped me so much! Thanks!

[@MariosMathTutoring]

Great! I’m glad my video was able to help you!

[@timemachinestudios8413]

me 2, fuck

[@jianghaoyoutube5017]

Thanks I finally understood

[@MariosMathTutoring]

Glad my video helped you!

[@wajahatkhan9455]

Thank sir!

[@MariosMathTutoring]

You’re welcome Wajahat!

[@wiv1473]

watching this right before my algebra 2 midterm. wish me luck

[@connorhernandez7772]

Really good teacher

[@MariosMathTutoring]

Thanks!

[@theojmandude3995]

Anyone else feel the chills when that marker hits the board?

[@Saeed-du2eq]

Thank you saitama for teaching us how to defeat the evil villain

[@yousefmohamed1381]

CLUTCHHH!!

[@MariosMathTutoring]

Glad my video helped you Yousef!

[@malviyagirl]

you look ethereal!!!

[@nwto235]

Thanks a lot teacher :)

[@MariosMathTutoring]

You’re welcome!

[@ballking6439]

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]

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!

[@hypehouse5457]

God bless you

[@MariosMathTutoring]

Glad you liked the video!

[@matthewjoseph236]

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]

+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]

Mario's Math Tutoring stretch by -2

[@pokinchui8632]

That is good , thx

[@MariosMathTutoring]

+Fresh M. Your welcome

[@muhammadfarooq2570]

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]

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!

[@matthewjoseph236]

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]

+Matthew Joseph yes that is correct.

[@matthewjoseph236]

The a value would be -2 so wouldn’t it be vertical compression by a factor of -2

[@MariosMathTutoring]

+Matthew Joseph The negative reflection over the x-axis and the two stretches it

[@daviddemar8749]

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]

Glad you liked the video David! Welcome to the channel.

[@naveensingh5787]

how to identify from given equation of function ,if it is one one ,many one etc

[@dannyhong7586]

Subscribed

[@MariosMathTutoring]

Welcome to the channel Danny!

[@user-su3qy]

U make it easier for me

[@MariosMathTutoring]

You’re welcome!

[@jt6170]

Thx

[@MariosMathTutoring]

You’re welcome!

[@demy4383]

wait for the square root of x + 2 problem why did we subtract 2 if there is a plus sign

[@wrenshere4711]

2 classes away from a quiz that imma fail. But maybe not after this 😂

[@MariosMathTutoring]

Glad my video helped you Wren! Good luck on your quiz!

[@eehub6710]

Sir ,can you pls tell why when we have a negative sign in the function, why the graph is shifted to the right???

[@MariosMathTutoring]

My Secret Math Tutor did a nice job explaining it in this video...go check it out: kzbin.info/www/bejne/pKCYan6AndOXnMU

[@eehub6710]

@@MariosMathTutoring than you very much for this sir😊🙏

[@yehhhboiii4005]

I dint really get half of this but thanks

[@elifnothing]

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.

[@walidrazzari609]

Bless❄️💯

[@Samir-rd8xp]

Im still a bit confused, what would the transformation be for f( x/5) and -f(x).

[@MariosMathTutoring]

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]

@@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)

[@koushikvallam9277]

The class was awesome but slightly increase font size 😊😊

[@miaaa8156]

THANK YOU IM STRUGGLING

[@MariosMathTutoring]

You’re welcome Mia!

[@dariousdennis5594]

Me: Maths without letters. Not me: Maths with letters.