Graphs You Must Know (Precalculus - College Algebra 13)

[@anim112]

U could really connect to people who are slow in maths. It's wonderful how you simplify and emphasize on the key points. Deep respect for you sir.

[@aypeezy]

i feel like you have to really like math to be able to explain it as well and effortlessly as this guy does and i appreciate that detail so much

[@Fazal828]

I'm in calculus 3 and this video is still VERY relevant. I never learned (or was even taught) any of this in the TWO PreCalc classes I took and it really came back to bite me during Calc 1 and 2. Thanks, Professor!

[@VarunVishwakarma1]

In INDIA we call Guru to a teacher, We touch their feet to give respect. Every time I see your video It simply comes from my heart to touch your feet. That has never happened to me throughout my life. You are simply amazing. I had a feer of Mathematics. Now it's gone. Thank you.

[@tanushst.michaels_high_sch3700]

Broo 😎

[@Verticalasymptotlover]

Feet fetish

[@Verticalasymptotlover]

Feet Fetish

[@proteopathy]

I am now in my junior year in electrical engineering but I still watch your videos to keep me fresh. You are a gentleman and a scholar, truly. Thank you so much.

[@Dontworryboutit247]

Love your videos. Please do a series on linear algebra. My Soul will thank you for eternity. Love you prof!

[@taekwondotime]

*Handy tip:* The curve on the graph will bend one time less than the exponent in the function. x^1: Doesn't bend at all. Straight line. x^2: Bends once. x^3: Bends twice. x^4: Bends three times. x^5: Bends four times. And so on.... :)

[@colchi2547]

Even functions all have parabolic shapes, thus they bend similarly

[@sebcodestheweb9385]

This is incorrect

[@sebcodestheweb9385]

It's like colchi says

[@taekwondotime]

@@sebcodestheweb9385 Can you list an example?

[@soupy5890]

that's how many times it *can* bend, not how many times it always will

[@OctoberMorningRain]

Thank you for actually explaining why the graphs are shaped the way that they are. This was not explained to me while taking college algebra. Now I am better prepared for calculus.

[@imanabu5862]

when I finish college I will be owing those youtube supermen and superwomen a lot! you saved me in high school and you are saving me again right now. I wish you get what want in life just like you allowed us to get what we wish by these videos

[@996dragonslayer]

I think you mean owe

[@Stephenc35753]

You are amazing. Im back in school right now at the age of 31. Your channel is the only reason im not completely lost (because my professor is very bad 😢). Thank you so much. I can't thank you enough.

[@tmann986]

I’ve been very appreciative how much work you put into this. I’m review my pre calc before this fall semester. I have calc 3 and Modern diff eqs. Kinda crazy haha thank you once again

[@narutorock998]

Thank you king! I have hope for myself in college algebra now 😭😭😭

[@BrainGainzOfficial]

Quality lookin' sharp! What kind of camera do you use?

[@thestormcraft4012]

likely a high quality video recorder that you could buy for like 500 bucks with a tri-pod.

[@georgesadler7830]

Professor Leonard, this lecture analyzes the graphs that all students in science and engineering students should know. Students should have a deep understanding of these graphs and their impact in mathematics.

[@socialonly4491]

Using all the best, positive and wonderful from the dictionary won't be enough, I can just say that I'am and will be grateful for ever. Thank you Professor Leonard, may GOD bless you and all that you love and care about.

[@letsbehappier740]

Thank you so much! pls never stop posting!!!!

[@ephraimcabiliza317]

Thank you once again Professor Leonard. You are phenomenal

[@rachelleb2007]

You are a lifesaver! I feel like a genius listening to you!

[@Dontworryboutit247]

DEAR PROFESSOR LEONARD, YOUR VIDEOS HAVE HELPED ME GET THROUGH HIGH SCHOOL AND COLLEGE. I’VE JUST STARTED LINEAR ALGEBRA AND I’M STRUGGLING GREATLY. THE TEXTBOOK IS ASKING ME ABOUT QUESTIONS THAT IT DIDN’T EVEN DO ANY SAMPLE QUESTIONS ON. PLEASE DO A SERIES ON.. INTRO TO SYSTEM OF LINEAR EQUATIONS. I NEED HELP WITH FINDING SOLUTION SET OF EQUATION(S) WITH MULTI-VARIABLE EQUATIONS SUCH AS ** x - 2y + 3z = 5** etc

[@wolfsschanze7061]

What an amazing guy you are.

[@AtomicMushroomz]

Brilliant video

[@shaunfrost8341]

Big fan your way of teaching sir..just made sem easier!!!love from india

[@marco39376]

thank you so much for the incredible lessons.

[@skillsetsociety]

You're literally superman teaching us math

[@narendraarya7800]

thanks a lot sir . u r helping masses in learning mathematics.

[@jeroincababat565]

I failed in Math(Calculus) in college because I took different field not related in STEM when I was in middle school. Now I'm here to finish all this course to fight back and pass that Calculus subject. Next I would take the Calculus course together with some textbook that I found in the internet.

[@manishpingale6558]

Love your videos! Please do a series on linear algebra.

[@Gaurav-rv3eh]

Damn, camera quality looking nice

[@wanyangqiao9829]

great summarize!

[@VieciTheengineerastronaut]

This dude is a LEGAND,

[@kingmali5897]

thank you so much sir. you really helped me

[@gleon1602]

The thumbnail is hilarious

[@insiya4561]

my life in short :)

[@Peter_1986]

He is like "hmmmm well um wait a moment, let's do that again".

[@Peter_1986]

Actually a lot of his thumbnails are hilarious. Most people look funny when you take a random snapshot of them like that, lol.

[@AvinashKumar-gm9gq]

Very understanding

[@madebyyuzz]

THANK YOU!!!!

[@bernardbethel5401]

“…can’t touch this…”😂

[@gamesonrack7138]

Thank you

[@fuzyfuzfuz2]

Thank you for spelling asymptote. Ive been spelling it acentote this whole time 😅😅😅

[@asdflkj2041]

Fantastic

[@lexibrad7476]

Love your video Professor Leonard! You have helped me a lot this semester. Next semester I will be taking Elementary Calculus. What serious would be best for me to study before going in to it?

[@ahmedistiaque6656]

Well, I was surprised when I landed in this challenge. Is Superman teaching us math? Yes, he is.. Thanks for all math helps. Professor Leonard

[@MrJohnnyCrock]

Me being "math illiterate" Prof: Does that make sense to you? Me: uhhhh... It is getting better but I still have a long way to go.

[@nikk4s]

I can't remember shapes of graphs. I can remember what defines the shapes. All but 2 of the graphs are variations of f(x)=x. f(x)=|x| is a piecewise function where y for -x is inverted. Most of the rest are described by the exponents of x. Square and cube roots are fractional exponents. The farther the exponent is from 1, the sharper the curve of the graph at its apex giving a more squared off line. The larger the exponent, the more the apex of the curve will move away from (1,1) toward the x axis making the line more vertical. The smaller the fractional exponent, the more the apex of the curve will move away from (1,1) toward the y axis making the line more horizontal. For function with x as the denominator, y is the reciprocal of x. I would love to see a video showing this and tying in transformations as a way to further tweak the line that exponents or a fraction created.

[@adityapathak2267]

Hi sir please make the video on LINEAR PROGRAMMING PROBLEM...THANK YOU

[@taekwondotime]

I hope he gets back to differential equations. :D

[@Ddd-rr3xk]

Saved this vets life.

[@PoppySuzumi1223]

x^2 is an even function parabola graph, 1/x is an odd function hyperbola graph.... so Professor Leonard what about 1/ (x^2) ? What is it ?

[@Spartans-community]

Professor actually I can’t understand how you take the curve of the graph.please can you explain it to me. That will be a great help!

[@GodGuy8]

I’m really getting into your videos to make custom indicators for forecasting in the stock market and I gotta say you look just like me man we could have been clones you’re probably about 10 years older than me I’m 25 I wish I would have taken math more seriously

[@JLiptak]

Question for students: Is function f(x)=b ever going to be odd function?

[@jimjim2119]

I wish I could take him for my college math teacher but, I live in NYS.

[@moviepics007]

i love u man

[@farahhammoud4477]

please upload the transformation video!!

[@Schoolboy141]

Professor, sorry for asking you here, but i can't find Calc 3 Lecture 14.5 video, is it missing or just it's just an listing mistake ?

[@olkkakanghono7408]

I am speechless

[@alikarimi2778]

but the output of negative roots are not real numbers that's what you told in previous videos

[@franciseylim11]

Sitting down here waiting for new video....

[@ProfessorLeonard]

Hi Francis! I took last week off for Thanksgiving, but I'll have a video today (if it ever finishes uploading)

[@franciseylim11]

Professor Leonard, can’t wait your new video.

[@rushyscoper1651]

1/x still fit -f(x) = f(-x) yet i said its not odd because it doesn't go through the origin, so which is it? does odd function need to cross the y-axis as while to be odd?

[@pkus]

it does not need to be go through the origin instead its has to be symmetric of the origin. Anyways, in other way we can prove that f(x) = 1/ x is odd function, f(-x) = 1/(-x) = -1/x = -f(x) so its odd function

[@churromister589]

Any updates for differential equations?

[@michaeljjan6344]

I am also curious about this.

[@ayushbhandari3230]

Can someone explain me That how does cube root of -1 is -1 . It should be an imaginary no. So there should not be any point in graph

[@paky3052]

-1 * -1 * -1 = -1

[@PastryDonut]

Root is the opposite of exponent. Try raising -1 to third power: (-1)^3 = -1 * -1 * -1 = 1 * -1 = -1

[@thatomofolo452]

[@austin.kallungal]

👑

[@krystinasaragos1535]

9:08

[@VarunVishwakarma1]

One request.. at the end of the video, if you could stand aside it would be helpful to take the screenshot

[@feilongish]

Complete

[@KishoreReddyMath]

Hi,I am interested to create and publish math video lectures on your KZbin channel

[@shahilshrestha3700]

sir looks like Henry Cavill 😂😂😂😂

[@dashaagafonova519]

be например you

[@netneutrality2024]

Graph you must know: Граф Монте Кристо.

[@taekwondotime]

*Handy tip:* The curve on the graph will bend one time less than the exponent in the function. x^1: Doesn't bend at all. Straight line. x^2: Bends once. x^3: Bends twice. x^4: Bends three times. x^5: Bends four times. And so on.... :)

[@tankebee4640]

Not true, x^n will have at most n-1 turning points. Note x^4 x^6 can look similar to a parabola