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.
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!
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.
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!
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! 😂
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!
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!!!
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 !!
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.
Hi professor, was wondering if you'll do a TTP video on certain mathematical methods not typically taught in class such as Fubini's Theorem for Gaussian Integrals.
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 🤗🤗
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?
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.
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!!!
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.
🎯 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
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
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.
This man really out here giving back to us kiddos. Thank you, Professor Leonard! Please never stop!
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.
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!
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.
Same! I’m just watching to see concepts my school brushed over before I start my stem major in a couple of months.
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!
We love your math videos. Thank you for all your hard work !!
Not all heroes wear capes!
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! 😂
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!
words cannot describe how much this video helped me
Really needed this thank you so much
Great class! Cant believe how cool math is.
Loving these videos man! Please never stop uploading these
Such a thorough yet simple explanation. Thank you again for all these videos. Such a great way to learn
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!!!
damn youre son is doing pre calc in 8th grade hell yea good for him
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
I really thought you were joking, oh my god.
Love the videos! thank you so much.
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.
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.
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 !!
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.
Thank you very much professor
Thanks professor leonard for teaching me mathematics in such a great way keep on making awsome mathematics playlists you're a global teacher.
Thanks for your work and refreshed memory
Hi professor, was wondering if you'll do a TTP video on certain mathematical methods not typically taught in class such as Fubini's Theorem for Gaussian Integrals.
Bravo Professor! Thank you so much!!
omg I wish this guy was my professor, he makes these so easy. Thank you so much
This lesson was really helpful 😮. I’ve been struggling with piecewise functions. Thank you Professor 🙏
This man is really good. He has made it more easier to understand
Never seen it taught with input output values but that was great. Thank you.
These videos are awesome man. Really helping me out rn. What is that shirt you're wearing? I'm trying to get one too
This math teacher is so handsome 🥺
Professor Leonard aka The goat
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 🤗🤗
This is my professor. Thank you, sir.
Hi Sir. Please can you make a video on Mathematical induction? Thank you very much.
i love you professor leonard
Really good,,,keep on going professor, I understood smth
Day 1 of calc 1 online and this video just gave me the confidence to not drop it. Thank you, Superhero Leonard.
u r a hero
I HOPE GOOD THINGS HAPPEN IN YOUR LIFE!!
You are the superman the GOAT
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!
Cheers!
i love you mr ripped
How do you know what the domains are? I'm confused. 8:43 why is the domain of f(x)= x2 x>0?
Your fan from India
22:25 is this x3. And 3x -2 function continuous?
Great
Are the domains for piece-wise functions given to you on a math problem or are we suppose to memorize them? x
8:32
always given to you
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?
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.
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!!!
"eenie meenie miney no" haha no don't do that
April/6/2022
April 5 2022
I'm a junior in highschool I've taken 2 weeks to try and figure this out and I can not get it
Why did you not graph f(x)=2 ; x=0 ? Good video,,,,Thanks.
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.
sir for -2x-3 apart from 0 can we plug in any other scalar like 1 or 2 for 38:00
and you didn't find the slope for that function too can i know why?
@@jahelhussleWe don't need to find the slope, because the equation for each curve or line is right there where you can see.
Please can you say Piecewise affine function instead of piecewise function?
8:47 : did he really just ask his mom to "pause right here" ?
Differential equations? :(
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...?????
Because the graph x^3 has those points, the cubic function.Plz review the topic of graphing function; it'll be helpful.
🎯 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
Prof Leo, why not include -4 at 37:00?
if you are referring to the last exercise, you can see that the -4 is included. it is why the circle is closed (colored black/blue)
Can some one clarify why cant 1 input have multiple outputs, Whats the issue here?
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
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.
❤From India 🇮🇳
oh hello sir
Enni Minnie mony lol 😂😂😂😅
graphing these are bitch. so much to know. ugh :-(
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!