Graphing Exponential Functions: Another Example

[@Sarah-bt8jo]

So much respect for this guy. He really makes it make sense.

[@ChristinaG-d3u]

I wish you were my teacher, like honestly!!! Your sense of humor is hilarious to me😂 i would HATE math but you explaining everything makes it crystal clear👀 thank you!!!

[@JonesyJay]

"It's a holey function. It's religious." 😂 You kill me.

[@Yunikoshi]

The way he said "Okay" in the beginning hahaha

[@catlady715]

+ButsniffBattles I needed that laugh. Went back to the beginning a few times just to hear it again....lol....

[@michaelwoodruff5752]

love it

[@burdiasdfghjkl8166]

your entire video set on exponential functions saved my letter grade! It didn't make sense in class but I get it now, thank you so much!

[@LinkedInstrategies]

why aren't we funding this! lol sidenote. Almost spilled my coffee.. Good stuff man good stuff.

[@anguspoole5998]

im learning so much thanks to you, you are something truely special and your teachings are great I now get B's in maths thanks to you and just wanted you to know that the world loves you legend and needs more people like you, have a blessing of a day you king and sending my love your way.

[@yasminesubaran3402]

"When in doubt, write it out" thanks so much!!!!

[@anneesamohamud1414]

thank you so much! i am a freshman i had a problem with this but now i understand so well! thanks to you

[@youtubeweb3009]

''WHEN IN DOUBT WRITE IT OUT'' - Dr.Burger lol ahhaha

[@sebon11]

This channel is so great!!!

[@anguspoole5998]

I agree he is a king from above

[@IreneBuclasan-v7x]

,😂ambot ui...kataw nmn lng ta mura isa...😅i like him when reading faster in exponents😂

[@lane9043]

"Junky Funky" ohmigoddd this is hilarious ty

[@IreneBuclasan-v7x]

The side note again mr.😂

[@initra25]

Thank you.... my current instructor just spits out equations at us. “a to power if 2 is all real numbers only if the denominator is the inverse of a rational.... or exponential function equal to the cube root of the sum of all numbers less than 5 but equal to any negative root of pie...... you should already know this equation before coming to class... you will never use it or see it again in any life application but you must know it”

[@bigstuff52]

You do great videos sir.

[@Mornys]

Could this property of exponential function of f.e. 2^x vs 2^(x+4) creating a narrowing band between them on the graph used to build some real life nanostructures. F.e. with using DNA-origamis one could start growing from two "roots" like 1 micrometers apart and then let them grow closer and closer to eachothers. Don't know what it would be useful yet, but the thought seems to tickle my intuition.

[@luisalvero3434]

awsome explanation for my quiz

[@shemaiahmariemojuntin5932]

you're awesome dude.

[@lavanyamandal247]

I have a doubt. Why are we shifting the function to the left. shouldn't we shift it to the right because we are adding 4 to x and not subtracting?

[@theguilty999]

Side note... lmao

[@NabilRouissi]

You are awesome! C sharp

[@Noah-ug7yp]

what if you had a function like this f(x)= 4(0.5)^x+2

[@aijanemahinay9344]

It's hard to Understand!😭 But thank you because I learn something

[@baboydamo6912]

May I ask, What does g(x) means??? and whats the difference between f(x) and g(x)??? Please help... thanks x'D

[@upradiocircle2005]

there's actually no difference, you can use whatever variable you want

[@jamestyson6767]

i think its just a strange way of writing y.

[@Travie_Law]

I like this guy

[@c.danielpremkumar8495]

16*2^x should pass through (0,1). Any number raised to the power x has to pass through the point (0,1)

[@jamestyson6767]

No, 2^x = 1. BUT then it is multiplied by 16.... SO it passes through 16, not 1.

[@loheyz4821]

Thank you

[@hannal4715]

why does he look like one of the wiggles

[@kayson598]

ok wait- so why did you shift the line to the left if it was positive???

[@spinnis]

ikr

[@westbays7283]

Thank you!

[@cyliachipara5658]

thank you so much

[@youtubeweb3009]

2:15 cuteeeeee

[@roidsmoddingteam7759]

All these people asking for answers to their homework lol

[@Noah-ug7yp]

thanks

[@richkrusajoe1500]

okay so let's try to graph some slightly more exotic exponential functions to get a feel for how the exponential function works and manipulating that object so let's begin by graphing f of X equals x to the I'm sorry two to the X plus four power now how would I do that well I basically see well actually there's two ways of thinking about this let me talk about both ways one way is to notice that in fact I see this is just basically two to the X but then I instead of X I have X plus four so that's just shift in the X which way add to X go west so it should be a shift this way so what I could do is the following I could take the picture of just two to the X so let me draw that in just slightly I'll dot that in so this is just uh this is just for us this isn't actually not you know part of the answer at all but this is a 2 to the X now what I do i take that picture and I'm going to shift it four units over this way I'm gonna shift it four units over this way this point is 1 so where would that go if i put in x equals 0 here I'd see 2 to the 4th so I see something really quite large so I'd see this so all I did there was take this picture and shift it four units this way so it looks like if the s sort of not as interesting the optical illusion right it looks like it's sort of wide here and then it's less wide here that's because you're looking at the height look at the distance this way this should always be the same it's always four units even over here it's four units four units I took this picture and slid it over four units so that's one way of seeing the graph of this and that's correct that's great and if you like it perfect another way actually would to be to would to be to use some laws of exponents here let me just point this out is a little side note get it side note I'm full of them okay and to realize that if I have two to a power that's the sum I could just write that as two to the x times two to the four because remember what you do when you have the same base we saw you add exponents and remember the slogan with exponents when in doubt write it out think about this I have two multiplied by itself x times then I have two multiplied by itself four times how many twos do I have X plus four so this is really okay well then you see this is just 2 to the 4th which is 16 times 2 to the X so then I could think about the graph in the following way I take this graph and just multiply it by 16 and what does that do it takes this point 1 and moves it up to 16 and then it takes this thing and sort of bends it up and it bends it over so then this is sort of now a what do we call this a shrinkin basically or expanding by multiplying this by 16 we see what happens that way so that's another way of thinking about it which is sort of worth sort of noting but I think the easier way to think about it is just think about it as a shift in the X for units this way okay now what I want to take a look at now I want to write the next question here because I want you to see the difference the next function I want to look at I'll call it G is going to be 2 to the X plus 4 and notice that is drew nicholae different from this this was 2 to the power X plus 4 this is to the x plus 4 so I take all this stuff and add 4 to it so what's that going to look like there that's going to be a shifting of the Y's because I just take the answer I got with the X is an ad for 2 everything whereas this was a shifting of the X's I've got to change the X by 4 and then figure out what Y is so here I start off with this picture and what do I do to it I just raise it four units up one two three four so in fact that picture would look dramatically different I would just take this picture and move it up four units so that's the difference between this kind of thing and this let me actually graph this right on the same axes exceeds I'd move this up four units this is by no means drawn to scale I apologize and this would be two to the X plus four whereas the purple thing I remind you was two to the X plus four so to get to that to get to the green what you did was you added four this way everywhere so took this picture and just raised it four units up and this picture I took it and raised it for a move to four units this way so make sure you see the difference between these two functions they're dramatically different if I take an expert exponential and add four to the whole thing that's going to be a shift upward if I take two to the X plus four then that's going to be a shift to the left by four all right one final note C sharp no sorry is what happens if I we look at something like this like minus three to the X well this is little tricky B's for example if I put in minus three squared that's okay I know what that means right that's going to be just minus three squared it's going to be nine what if I look a minus three to like the one-half power well that's the square root of minus three and that's not a real number and as you can see any time I have a fractional exponent that has an even denominator that will be some sort of root that I couldn't take so in fact this is just complete garbage as a function so junky function junky funky so in fact we will never ever look at functions that have a negative thing in here and why because it won't be defined at a lot of places I owe to be it be a very holy function to be a religious function to be very very holy because it would be all these points where you just wouldn't have things there just be all dip dip dip dip so we don't even look at that never never never now for those of you who might say wait a minute isn't this just equal to this well those people are sadly sadly sadly mistaken these are not equal at all this is -3 raised to the X power this is 3 raised to the minus X power this we will never graph this is false this we will never graph this we can always graph because that's just one third to the X so the only kind of basis we're allowed to have that make sense to have our positive bases they could be less than one they could be bigger than one but they can't be negative all right I'm glad I got that in my system

[@laptopuse2689]

me when the

[@gor5048]

side note

[@carolo6098]

is he athiest or sum lml

[@mohittiwari4083]

Nice sir please give contact

[@talhaahmed6980]

This feels like a cheesy 90's video.

[@TheAdoonAlle]

he is extremely helpful to so many people including me, so buzz off rude!