One to One Functions (Precalculus - College Algebra 50)

What one-to-one functions are, how to determine one-to-one-ness, and why they are important to inverse functions

[havaneseday]

Finding your channel has given me a wealth of knowledge. Ill be going back to school in 2 months at the age of 36! I've been studying up, while still working full time at my current job. |
Pretty much started from Grade 9 algebra and up. Currently half way through a Coursera Pre-calculus course I purchased at the start of last year. I am running into some problems that require extra attention and readings but they don't offer an additional resources. After a quick YT search, I stumbled upon your channel and I'm blown away. This is exactly what I was looking for!
Thank you for taking all this time and effort into putting these videos together. It has been so very helpful.
You rock Professor Leonard!!

[AyyyGEEZER]

I just wanna say thank you, Professor Leonard. I am currently learning from your videos about continuous random variables and normal distribution (8 years ago) and I came to this video to see how your older videos compare to your new ones. The fact that you are still able to engage your audience with optimism while explaining the topic in a clear and understandable way is truly impressive and should not go unnoticed, especially during this time when you may not be teaching in a physical classroom with students that you can directly interact with. Keep doing the amazing job that you are. Millions of students around the world appreciate you.

[Tirthankar]

50 videos into this playlist and I really want to thank you from the bottom of my heart prof Leonard. I am learning so much because of you. Thank you so much

[Heavenlight]

Thank you for all your work Prof. Leonard. As a fan of your channel I cannot wait until this precalculus series is completed. I think it will be one of your best series so far. You have already 50 high quality videos and not even started with geometry.
After this series and dif. equations I hope that I can also enjoy a new series on the topic of linear algebra. Keep it up, I continue supporting you on patreon.

PS: Best thing to do is learning from you while covid, instead of watching too much useless youtube or netflix.

[acentasecond]

really good video on one to one functions, something i struggled with early on in my studies!

[rosepierce]

1:06 Unfortunately, Clark Kent exists.

[brandonestrada]

I cant wait until this gose viral and thousands of girls get the hots for this guy

[georgesadler]

Professor Leonard, thank you for another awesome video/lecture on One-To-One Functions. The horizontal line test really shows if a function is one-to-one or not.

[michaeljjan]

I'm pretty sure that 007 is James ID number, you have to change that part.

[emmalove]

Thank you professor Leonard. I am learning alot from your teaching

[Mark-vlzm]

I can't wait until you get into trigonometric identities, addition and subtraction formulas, double angle, half angle, etc.

I always struggled the most with proving/verifying identities. I never know which side to work on or how to effectively and efficiently tackle those problems..

Edit: Thank you for all the videos they have really helped me with my Pre-Calculus class so far!!

[Aminhelal]

You are great professor Leonard, you helped me a lot with functions thanks a lot

[yasmineyasmine]

Thank you very much, you helped me a lot!

[dragmahk]

You deserve a nobel prize in education

[ginamartin]

I hope you realize your true teaching abilities. No joke, one out of too many whom do not.

[Herlongian]

A horizontal line is the is the best way to show different x values can have the same y output and be a function. Nothing passes the vertical line test better than a horizontal line. BTW—x axis is y=0.

[somasahu]

There are 2 dislikes, they were identical twins !

[SilentEagle]

Almost halfway through the series on my way to calc 1, then 2, then 3! Hopefully you start linear algebra by the time I'm finished with calc 3 (^-^)

[ginamartin]

Thank you ProfLeonard. I have had such a hard time with algebra due to not having practical examples to make it click in my brain. I have to see points a-b. Your explanation separates you as a true teacher from a person whom has the degree to teach only because they know the steps but do not know how to explain the practical interpretation/reasoning (teach) not realizing that those they have the responsibility to teach may not have the gifted learning knowledge in mathematics.

[Peter_]

Is it correct to say that a one-to-one function always has a positive or negative derivative?