How to Graph Piecewise Functions (Precalculus - College Algebra 12)

[@JohnHobitakis]

This method of learning is so much better than sitting in a live class. It's cheaper, not restricted to a specific time, do not have to commute, can pause & rewind. Additionally your teaching style is great, I really appreciate these videos.

[@thegamingpro9128]

This man really out here giving back to us kiddos. Thank you, Professor Leonard! Please never stop!

[@jasonsmith7809]

Holy Moly! Im 53 with a PhD and never really learned this the right way. I wish I had you as my high school teacher. It makes so much sense. Thanks for your dedication!

[@shmergosm687]

I liked the class-room experience of your videos with the students in the background, but this new style to me is way better! also, about to purchase a decal to support, I already passed pre-calculus but watching these videos I'm actually learning & understanding why these things are being done! thanks for everything.

[@silverdove9911]

Same! I’m just watching to see concepts my school brushed over before I start my stem major in a couple of months.

[@jakichaaan452]

Somehow I couldn't grasp the idea of finding domain and range and looking at a piecewise graph and making a formula for it. Im watching this to review before my exams and it was very helpful, thank you!

[@mattdrafted2024]

We love your math videos. Thank you for all your hard work !!

[@krystinasaragos1535]

So here I am, 12/15. I’m catching up. I just wanted to let you know that I enjoy this style of videos where you are talking to the camera instead of the actual students like you did with the calculus playlist. Also, you look a lot like Patrick Wilson. I actually Wikipedia-ed him to see if he has a brother who is a math professor! 😂

[@ProfessorLeonard]

Hi! I'm glad you like the new style of video. I wasn't so sure in the beginning, but I rather like it now. Seems less distracting for the viewer. Good luck!

[@IncognitoSprax]

I got here by searching "buff math teacher" out of curiosity as all the math people at my uni are out of shape or just skinny

[@tzeentch8228]

I really thought you were joking, oh my god.

[@jenniferfarrelly]

My son is really struggling with this, so I watched you to help him out. He has a test today and I think this helped me help him. He's in 8th grade by the way!!!

[@marcelocastillo1238]

damn youre son is doing pre calc in 8th grade hell yea good for him

[@dclaila]

words cannot describe how much this video helped me

[@Anwell100]

Such a thorough yet simple explanation. Thank you again for all these videos. Such a great way to learn

[@georgesadler7830]

Professor Leonard, thank you for a clear explanation on how to Graph Piecewise Functions in Precalculus and College Algebra. College students should really appreciate this style of teaching because the teaching styles are all different everywhere.

[@astudilloerika31]

Thank you so much! I have an exam coming up and honestly I feel like my professor speaks a different language. This helped me understand so much more.

[@joannekangalee3281]

Really needed this thank you so much

[@manishpingale6558]

Loving these videos man! Please never stop uploading these

[@scientificamankwaah9339]

This man is really good. He has made it more easier to understand

[@arsdwalos6840]

Not all heroes wear capes!

[@00Noontide]

Great class! Cant believe how cool math is.

[@Whd29393]

This math teacher is so handsome 🥺

[@renad-vt5rt]

🎯 Key Takeaways for quick navigation: 00:00 *📊 Understanding Piecewise Functions* - Piecewise functions consist of multiple defined segments or pieces with specific conditions for each segment. - Key points include understanding what piecewise functions are, how they work, their domains, and how to use them. 01:25 *🔄 Evaluating Piecewise Functions* - Piecewise functions involve using specific pieces of the function based on the input's domain. - Evaluating piecewise functions entails identifying the domain interval for the input, then using the corresponding piece of the function to compute the output. - Each input must have only one output, adhering to the fundamental concept of a function. 08:36 *📈 Graphing Piecewise Functions* - Graphing piecewise functions involves understanding the domain intervals for each segment and graphing them accordingly. - The x-axis is separated into intervals based on the domain of each function segment. - By plotting each segment within its respective interval, the graph accurately represents the piecewise function's behavior. 18:05 *📈 Graphing piecewise functions: understanding endpoints and open circles* - Understanding the concept of endpoints in piecewise functions. - When there is no equal sign, do not include the specific point as an endpoint. - Use open circles to represent endpoints that are not included in the function. 20:25 *📊 Graphing piecewise functions: graphing individual pieces* - Separating the domain into intervals and identifying the pieces for each interval. - Graphing each piece separately while considering endpoints and boundary values. - Understanding the graphical representation of piecewise functions on specific intervals. 25:31 *🔄 Graphing piecewise functions: continuity and discontinuity* - Explaining continuity in piecewise functions and identifying discontinuous points. - Understanding how to graph discontinuous functions and the importance of open circles for discontinuous points. - Highlighting the difference between continuous and discontinuous piecewise functions. 37:36 *📈 Graphing Piecewise Functions: Initial Steps* - Graphing piecewise functions involves understanding intervals and their domains. - Identify the y-axis intercept and slope to plot the function accurately. - Utilize boundary values to determine open or closed circles on the graph. 41:08 *📊 Handling Boundary Values in Piecewise Functions* - Even if not explicitly stated, use boundary values to determine points on the graph. - When boundary values are excluded (no equals sign), represent them with open circles. - With boundary values included (equals sign), represent them with closed circles. 43:59 *📉 Graphing Piecewise Functions: Putting It All Together* - Piecewise functions are composed of segments defined by their domains. - Boundary values help determine continuity and the nature of points on the graph. - Understanding the interplay between intervals, boundary values, and graphing ensures accuracy in representing piecewise functions. Made with HARPA AI

[@psoren423]

Never seen it taught with input output values but that was great. Thank you.

[@octaviasithole3621]

This lesson was really helpful 😮. I’ve been struggling with piecewise functions. Thank you Professor 🙏

[@MelsMars25]

omg I wish this guy was my professor, he makes these so easy. Thank you so much

[@rayj1232]

Professor Leonard aka The goat

[@SonuSingh-qw2bs]

Thanks professor leonard for teaching me mathematics in such a great way keep on making awsome mathematics playlists you're a global teacher.

[@ElixTMOV]

Thank you professor leonard, thank you for everything you have done for us, you are the greates math teacher I have every gotten a chance to study from 🤗🤗

[@ardaberk980]

İ am from turkey but i swear i just understand from you, god bless you

[@philosophertiger4124]

I'm going to try and watch all the way up to video 20 this week. Thankyou professor for all of the great content. I am doing a lot better in math.

[@AjikawoAdebayo]

This is my professor. Thank you, sir.

[@techzoneplus]

Excellent Explanation, Thank you so so much

[@wanyangqiao9829]

Thanks for your work and refreshed memory

[@aimansiddique6246]

kudos to you for putting in so much hard work and effort to teach strangers on youtube, though I wonder why your channel doesn' t come further up in the search fro calculus, since these are pretty exhaustive series. I needn't look anywhere else for these topics, just completing your series is enough to give me a good understanding. thanks again !!

[@cristhiangarcia5991]

Love the videos! thank you so much.

[@pebbled2303]

These videos are awesome man. Really helping me out rn. What is that shirt you're wearing? I'm trying to get one too

[@JULIEDELARO]

Day 1 of calc 1 online and this video just gave me the confidence to not drop it. Thank you, Superhero Leonard.

[@ethioupdatedinfo.]

Thank you very much professor

[@Dontworryboutit247]

FOR THE LOVE OF JESUS CHRIST, PLEASE MAKE A SERIES OF TUTORIALS ON LINEAR ALGEBRA. I’M SUFFERING OVER HERE. PLEASE, FOR THE LOVE OF HUMANITY DO A SERIES ON LINEAR ALGEBRA. THE WORLD WILL THANK YOU FOR THAT.

[@PracticalHealingFoods]

Bravo Professor! Thank you so much!!

[@kiropalex1786]

Really good,,,keep on going professor, I understood smth

[@kkfg3008]

i love you professor leonard

[@jeroincababat565]

You are the superman the GOAT

[@Joker-2357]

Your fan from India

[@selamuTse]

I HOPE GOOD THINGS HAPPEN IN YOUR LIFE!!

[@justbraks]

Hi Sir. Please can you make a video on Mathematical induction? Thank you very much.

[@kbryyl9378]

u r a hero

[@Briskybroski77]

22:25 is this x3. And 3x -2 function continuous?

[@krystinasaragos1535]

Are the domains for piece-wise functions given to you on a math problem or are we suppose to memorize them? x

[@krystinasaragos1535]

8:32

[@ProfessorLeonard]

always given to you

[@mercantilism954]

How do you know what the domains are? I'm confused. 8:43 why is the domain of f(x)= x2 x>0?

[@flaws9288]

i love you mr ripped

[@YouTubetrash-w8i]

sir for -2x-3 apart from 0 can we plug in any other scalar like 1 or 2 for 38:00

[@YouTubetrash-w8i]

and you didn't find the slope for that function too can i know why?

[@JuanPabloMartinez-b8m]

​@@KZbintrash-w8iWe don't need to find the slope, because the equation for each curve or line is right there where you can see.

[@malekstudies0944]

Hey! Love the lectures. Are you using any specific book for the course? if yes, can anyone let me know what book it is? thanks!

[@hirzaii]

I still don't understand the interval domain, I mean how do you calculate three over one then in the second function two over one. Pls help!

[@Trampflick]

Only thing I didnt understand is why the slope was over 1: 2x over 1; 3x-2 over 1;-2x-3 over 1. Why is that the slope...why is it over 1. Why is that the slope if. I understand slope is (y2-y1)/(x2-x1)....but why is it only the first x value and why over 1?

[@frustratedmf54]

I think this is from equation of line, y = mx + c, so in this case, m=3. Now, slope is rise over run, i.e. m=rise/run, where rise=y2-y1 & run=x2-x1. We already have m=3 which is nothing but m=3/1, so our rise=3 and run=1, which essentially means that you'll move 3 units up on the y-axis and 1 unit right on x-axis.

[@serafin8541]

With the dotted line we could say that VISUALLY the f(x) axis has shifted, am I right?

[@yeowonlim5285]

Can anyone recommend what kinds of texts book I can study with this precalculus lecture?

[@wesrobertson8753]

Cheers!

[@susanshweyeebo2677]

I didn't understand the last part. Why x+3 didn't use slope? I think (-4,-1) have to go down for -1 and goes right for 1. In other straight line , it used like that. But why not in x+3? Please explain it for me!!!

[@bookert.w2022]

Why did you not graph f(x)=2 ; x=0 ? Good video,,,,Thanks.

[@smoothacceleration437]

8:47 : did he really just ask his mom to "pause right here" ?

[@18harshraj61]

❤From India 🇮🇳

[@hyperkurisu2665]

How do we know what to plug in?

[@BONTUTESFAYE-g5b]

i dont get it why you choose (0,0),(1,1),(-1,-1) to find the graph of x^3 function i really dont get it could you answer for me...?????

[@basraashkir4041]

Because the graph x^3 has those points, the cubic function.Plz review the topic of graphing function; it'll be helpful.

[@zeeshan7372]

Great

[@GaminYoon1]

"eenie meenie miney no" haha no don't do that

[@ayushjaiswal4449]

Enni Minnie mony lol 😂😂😂😅

[@zeeshan5146]

April/6/2022

[@tenacious5735]

I'm a junior in highschool I've taken 2 weeks to try and figure this out and I can not get it

[@gradhd4359]

April 5 2022

[@collinskwadwoboateng5603]

Please can you say Piecewise affine function instead of piecewise function?

[@michaelfuxeklint4909]

I don't see any problems to add points on points, just make it a bit bigger circles, in reality you can put how many lines you want one on another no ......??, just a bigger circle for each 🤔🤔 (😪)

[@CoolMachination]

Can some one clarify why cant 1 input have multiple outputs, Whats the issue here?

[@anthonysummit3098]

think of a function as an mechanical machine (picture something similar to whats inside a clock) now all parts are fixed and they follow a certain pattern every time. Thus, when you plug in a certain number it should only give you one output and not multiple as all the mechanics inside the function are fixed and does not change

[@paulmaggiar8274]

Think of a calculator. You input 3+5, how many outputs does it give you? Just one, 8. How many inputs can you plug in to get 8? You can plug in many inputs to get 8.

[@tzuyu8788]

oh hello sir

[@NOO-ray]

are you related to Henry Cavill?

[@churromister589]

Differential equations? :(

[@Shes.naomii]

Why he lowkey....

[@thatomofolo452]

hi

[@taefalotaibi8071]

يالبيه اركز على الشرح او عليه

[@xbl4ck7]

graphing these are bitch. so much to know. ugh :-(

[@rickhoro]

Love your math lessons, but this was too obvious to have spent 45 minutes. 10 minutes would have sufficed., imo. Really do appreciate these, though!