Graphing Exponential Functions with Transformations (Precalculus -College Algebra 53)

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Thank you for always helping us, sir!😊

you are the reason I am passing my class. thank you...

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!

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I literally learned this Friday

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The best teacher ever, no questions asked.

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Is this series of pre calc going to be similar to my college pre calc course?

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I start giving this man a like before even watch the video

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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?

teacher you are the best

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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.

So much patience, so much passion, the best Professor ever! Thank you so much!!

Excellent presentation.

Great explanation and ideas for plotting . Thank you so much!!

Absolutely gr8

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?

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

Mar 02, 2023

Thank you professor Leonard !!!! Great video

well done!!!

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?

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.

im jealous of the size of my mans whiteboard

you always deliver it explicitly leonard