Introduction to Graph Transformations (Precalculus - College Algebra 14)

How to use Transformations to Graph basic functions and why the transformations do what they do.

[Tirthankar]

We should all be thankful that people like him exist in this world.

[averageyoutuber-kkly]

out of all my math teachers from various colleges and high schools, you teach math how it is suppose to be taught. not just how to do things but why you do it and what is actually is. well rounded lessons = actual learning and not just memorization. 11/10

[ammishtandon]

I had my Calculus 3 exam this week and I rocked it because of your lectures..You are phenomenal.. You teach with so much interest and passion, and not like any dull teacher, which motivates us as well to study with passion and to be honest your lectures made me fall in love with calculus...I'll be taking differential equations in the next semester, so I request you to please continue that as well when you have time..Hats off to an amazing teacher..I TRUST THE LEONARD!

[MahdiSadeghi-lyth]

Dude I dont know how to thank you. You are one of the very few people who really care about why something happens and dont wanna just memorize. Your lecs are an inspiration for other people to understand why logic and reasoning matters.

[TheDemarie]

THANK YOU! THANK YOU! THANK YOU!! I am a nontraditional student and I have never seen math like this. I have been staring at my 113 homework for three days trying to figure this out. This one video has helped me understand. I will be using any and all of your videos to finish my course. Thank you again. I have tears in my eyes from the relief of understanding it finally.

[Vice]

I rememer watching Prof. Leonard videos two years ago when I was talking Calculus. Thank you🇯🇲🇯🇲🇯🇲

[angelinastudy]

I am in high school in Russia. you explained the topic in 40 minutes better than my teacher in a week. Thank you

[kjpillay]

Best Math teacher on YouTube. Really grateful for the time you took to make these videos. You are helping generations of aspiring students. Not sure if teachers are aware just how much they change the world simply by doing what they do. Thank you Sir.

[drdr-nbmp]

All I can say is thank you for teaching with passion and explaining why things are what they are. Lot of academia live and thrive on theory but forget before theory comes hypothesis and if there is hypothesis there is always an idea and this idea is needed by someone that was in your head when you formulate or observe it so you shouldn't expect him/her to just understand your theory which is what was used to verity and proof your idea.

Your way of teaching has make me to understand, love and find a way to apply mathematics to many problem Ex is realizing this is how vector scalar, vector addition, subtraction, rotation, transformation is derived and use in graphics.

This is a light bulb moment for me and now I just understand and conceptualize what I already have an idea of but now my idea just turned to deeper understanding this is huge for me. Phasing shifting, phase lock loop all used in digital electronics are derived from this concept and you just demystify it all in first 10 minutes of a video that's not even calculus or solving any equation yet but ideas of what to come. Thank you, thank you and thank you!!

[reginavanata]

"You need to get your shift straight" haha.

[kabulkhan]

I can’t even begin to explain how much your lectures meant to me..💓

[skippytheelder]

It's amazing how you turn something that I always saw as complicated and you explain it in a simple yet completely accurate way.

[TabethaMartinHoward]

great professor me and my peers use his videos since our teacher is out because of injuries. he makes it really easy to follow and understand. i got a 87 on my exam just by following his professor! Wish me luck on the next exam.

[adomseddies]

I think I have found the mathematics teacher I had been looking for all this while. With much appreciations prof

[shanesmith]

Prof Leonard, I'm really glad you are young because it would be great if you could do videos for all math subjects over time. For example, I made it through abstract algebra but didn't really learn much because they didn't explain it well. It seems really interesting the "if this then that" and the logic study behind proving things such as the square root of 2, etc. We really need your intelligence and excellent teaching even more for the abstract stuff. It would be great to have you do an abstract algebra video and continue on with higher level classes as you progress. Of course, I'm enjoying your videos as you progress through all math subjects starting with the fundamental classes and on upwards. Thanks and I hope you'll forever continue with all math classes and subjects up to upper division and advanced classes. Thank you for all!

[CT-rwrw]

came to your most recent video to comment this.
currently taking calc 2 and have been watching your calc 2 playlist. Because of you, for the first time ever, i really enjoy doing math. We all appreciate you more than you will ever know.
thank you

[AB-cnhb]

Professor this transformation oddly enough helped me to understand linear algebra transformation. I really appreciate it.

[haven]

Holy crap, using the birth year analogy for the horizontal shift is GENIUS. Tysm for these videos!

[sfrank]

The moment professor leonard started talking about the input value for function or output value for y which is outside of function - it literally makes everything clear to me


for outside of function = ( 1, 1) become ( 1, 1+k)

for inside the function = the same (1, 1) becomes 1+k for every value of x which actually makes the entire x axis translate +k unit.

His explanation for key points for assessing the basic characteristic of graph is millions times better than all of the jargon i have gone through which involves mere emphasis of cramming on this notion

boundlessly grateful for him for doling away such insightful, simple and intuitive lessons - infinite times better than any of the content i have gone through in class or on internet.

effect of "Input value or output value" of the function is the main gist of understanding this

[niki]

More than the educational content and explanations, my learning quality depends on the vibe i get from the teacher. I felt realy relaxed and confident while listening to you which doesn't happen often! I hope the positive energy and my gratitude reaches you:)