Professor Leonard has been for many years one my preferred teacher on the web for my passion to re-learn calculus, now I watch his videos for my daughter in high school. I wish every student could have a Professor Leonard! Thx! From Italy.
Professor Leonard, thank you for another incredible video/lecture on Graphing Exponentials with Transformations. Transformations can make graphing much simpler, however it can be somewhat confusing.
Thanks Pro. Watching your videos has made me qualify for my upcoming exams for precalculus this coming November. You are the best..🤝. You are the best Pro.. I learned more from you than my lecturer. May the creator bless you for excellent work..from Africa
Thank you so much for the videos. I understnd things so much better. You are the best! I am looking at your last example and am confused. It shows on the video that a power of -x applies to x and so you made your x coodinate negative from 1,e to -1,e. However if you have a function e^2x and if you apply the same rule of multiplying the x coordinate by 2 then it does not work. Can you please explain?
I was confused too and I believe you are correct. I guess this video taught us two things: how to plot graphs and the fact that Professor Leonard is indeed not a god, but a hooman.
I got two questions now... 1) How do you know what the maximum x value is as the y value approaches infinity? 2) How do you get an equation where the curve happens between a large difference of y values compared to x values? (E.g. range of y=0 to y=1,000,000 and x=0 to x=100) I'm trying to find an equation that starts at (0,0) but pivots upwards where y values approach infinity as x approaches 100. Is this possible?
so question here...in the last function (23:35) how is "3" a stretch and not a horizontal shift? in my mind the 3 is taking the place of the "1" in the previous function f(x)=1-2^x+3
the 3 is being multiplied with the f(x) which is the y axis. Now that being said, a vertical stretch will be a horizontal compression (there is no escaping this and professor Leonard mentioned this in one of the previous videos ). Think of it this way, if you pull something vertically it must also compress horizontally. It reminds me of the bugs bunny cartoons
Could someone correct these if they’re wrong, because I need to remember the general form of each transformation, I would say they’re: 1) f(x)-2 2) f(x+2) 3) -f(x+1) 4) 1-f(x+3) 5) 3f(x) Any corrections or help would be appreciated!
what exactly is your doubt are you asking about what would be the transformations to those functions ? I didn't get it... if you are asking about what happens to those functions written by you then . f(x)-2 = Down shift by 2pts f(x+2)= left shift by 2pts -f(x+1) = left shift by 1pt and reflection about x axis 1-f(x+3)=left shift by 3 pts, up shift by 1pt, reflection about x axis 3f(x)= stretching the output vertically 3 times ( key points output *3) Now I need someone to check whether I transformed it correctly or not...
The best teacher ever, no questions asked.
Haa sxb
Maxaad barataa
Bro I am not learning now, my days of learning are in the past, but I recommend this video to my children.
Professor Leonard has been for many years one my preferred teacher on the web for my passion to re-learn calculus, now I watch his videos for my daughter in high school. I wish every student could have a Professor Leonard! Thx! From Italy.
I revisited calculus too her my daughter finishing her hs maths - thx again
Thank you for always helping us, sir!😊
hes amazing
you are the reason I am passing my class. thank you...
same!
So much patience, so much passion, the best Professor ever! Thank you so much!!
man you really deserve more then what you get in youtube
I start giving this man a like before even watch the video
Professor Leonard, thank you for another incredible video/lecture on Graphing Exponentials with Transformations. Transformations can make graphing much simpler, however it can be somewhat confusing.
teacher you are the best
Prof Leo bravo your last stretch was brilliantly described thank you
You are a life savior!!
Thank you so much sir
Thanks Pro. Watching your videos has made me qualify for my upcoming exams for precalculus this coming November. You are the best..🤝. You are the best Pro.. I learned more from you than my lecturer. May the creator bless you for excellent work..from Africa
He's amazing!
Excellent presentation.
Great explanation and ideas for plotting . Thank you so much!!
Thank you professor Leonard !!!! Great video
you always deliver it explicitly leonard
Absolutely gr8
Is this series of pre calc going to be similar to my college pre calc course?
Maybe all most everything is similar to my college pre calc course : )
The best professor
Thank you so much for the videos. I understnd things so much better. You are the best! I am looking at your last example and am confused. It shows on the video that a power of -x applies to x and so you made your x coodinate negative from 1,e to -1,e. However if you have a function e^2x and if you apply the same rule of multiplying the x coordinate by 2 then it does not work. Can you please explain?
Thank you !!!!!
My man.
For -3^x+1, would that not technically give us (0,0)? Which isn’t asymptote ?
-(3)^0 = -1, -1+1 = 0 or am I not doing something correct here?
I was confused too and I believe you are correct. I guess this video taught us two things: how to plot graphs and the fact that Professor Leonard is indeed not a god, but a hooman.
well done!!!
Thanku sir ❤️
we should collab one day professor i love your content!
I got two questions now...
1) How do you know what the maximum x value is as the y value approaches infinity?
2) How do you get an equation where the curve happens between a large difference of y values compared to x values? (E.g. range of y=0 to y=1,000,000 and x=0 to x=100)
I'm trying to find an equation that starts at (0,0) but pivots upwards where y values approach infinity as x approaches 100. Is this possible?
I literally learned this Friday
so question here...in the last function (23:35) how is "3" a stretch and not a horizontal shift?
in my mind the 3 is taking the place of the "1" in the previous function f(x)=1-2^x+3
the 3 is being multiplied with the f(x) which is the y axis. Now that being said, a vertical stretch will be a horizontal compression (there is no escaping this and professor Leonard mentioned this in one of the previous videos ). Think of it this way, if you pull something vertically it must also compress horizontally. It reminds me of the bugs bunny cartoons
💯💯💯
Could someone correct these if they’re wrong, because I need to remember the general form of each transformation, I would say they’re:
1) f(x)-2
2) f(x+2)
3) -f(x+1)
4) 1-f(x+3)
5) 3f(x)
Any corrections or help would be appreciated!
what exactly is your doubt are you asking about what would be the transformations to those functions ? I didn't get it...
if you are asking about what happens to those functions written by you then .
f(x)-2 = Down shift by 2pts
f(x+2)= left shift by 2pts
-f(x+1) = left shift by 1pt and reflection about x axis
1-f(x+3)=left shift by 3 pts, up shift by 1pt, reflection about x axis
3f(x)= stretching the output vertically 3 times ( key points output *3)
Now I need someone to check whether I transformed it correctly or not...
👍
OMG
im jealous of the size of my mans whiteboard
Mar 02, 2023
Don't yell at me!
Who is, my dude?