Graphing an exponential function with e as the base
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- Опубликовано: 2 окт 2024
- 👉 Learn how to graph exponential functions in base e. An exponential function is a function whose value increases rapidly. e is a constant called the exponential constant equal to 2.7183... To graph an exponential function, it is usually useful to first graph the parent function (without transformations). This can be done by choosing 2-3 points of the equation (including the y-intercept) and plotting them on the x-y coordinate axis. After graphing the parent function, we can then apply the given transformations to obtain the required graph.
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Organized Videos:
✅How to Graph Exponential Functions
• How to Graph Exponenti...
✅How to Graph Exponential Functions with e
• How to Graph Exponenti...
✅How to Graph Exponential Functions | Learn About
• How to Graph Exponenti...
✅How to Graph Exponential Functions with Stretch and Compression
• How to Graph Exponenti...
✅How to Graph Exponential Functions with Vertical Shift
• How to Graph Exponenti...
✅How to Graph Exponential Functions with Horizontal Shift
• How to Graph Exponenti...
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I see people giving a lot of flak on this video. I just wana say for anyone watching this, Professor McLogan isn't usually like this. I've watched a ton of his other videos and he is pretty much the reason I'm passing my pre-calculus course right now. He is just having an off day. If you are watching this because you are struggling in pre-cal then subscribe and keep going he is really good.
+Dylan Townes thank you, yes, I record myself everyday and do not cherry pick my best videos or when I am in my best mood. Unfortunately some videos are better than ever but I upload them all as I know someone may benefit from each of them. Happy that you appreciate them and happy to be able to assist you this year. Keep up the hard work and I will keep on making videos
im having trouible with precal. its so bad that the class named a group chat called surviving knodoel ( the teacher) lol
You're a great teracher I've been reviewing this concept for the past week in order to familiarize myself with my upcoming final but after this video I'm confident to say the least in graphing for exponentials. Thank you Sir 🖒
you are very welcome! happy to be able to assist you!
Great idea ..to graph tranformations..thank you somuch for giving clear understanding on drawing graphs
I've watched several of your videos and they are usually very helpful. But this one should have never been put up. You explained something wrong, then explained it wrong again. Then when you corrected yourself, you got irritated with your student because you confused the hell out of them. This should be redone!
deanna parnell I make a lot of videos, and yes am prone to making mistakes just like everyone else. I can tell you I am not irritated at a student for not understanding but probably at myself for not explaining it correctly. Not my best video but keep it up to show that yes even myself who makes 20+ videos a day are going to have off days, hours and explanations. I hope you don't get this impression from my other videos
You seem like a good teacher but i recommend when you make a mistake explain what you did wrong thoroughly because you lost me there
my mistake was that I forgot the y-intercept was (0,a) for exponential functions. that is why I changed the y-intercept from (0,1) to (0,2)
Thank you i should be ready for the retake now
wow....he is great...he really just goes into it!
understand it so much better now...brilliant teaching...💕
thank you! happy to help
i love this man, he does so many videos that saved me
Brilliant explanation sir.
to clarify when you say 4 to infinity for the range do you mean not including 4
yES
My summer calculus homework became a lot easier thanks to your explanations and lectures, so I thank you for your valuable contribution :”) You’re awesome Mr. McLogan!
happy to be able to help ShiRuVii!
Will 9 also be an asymptote?
Just wanna say thank you for making this video, helped me a lot Mr McLogan!
you are very welcome Sahel!
Can't wait to have money to buy one of your t-shirts
i loved the video but im a little unsure of how the y intercept could be 2, and yet the y asymptote is 4? there's been some mistake in the working out because there y intercept should always be higher than the asymptote
Why are math teachers usually bold
Dear Mr. McLogan. I just finished watching your video and i found it was very helpful to me. Your explanation is very good. i want to ask you one thing. How can determine the domain the exponential graph?? my teacher explained me many times but still i don't understand. Hope you can help me out. Thank you in advance
monika piseth If you are looking at the graph of an exponential function you will notice that the graph expands to the left and to the right indefinitely. Meaning there are not any values of x that are not apart of the function so the domain would be ALL REAL NUMBERS. However the range is different. For an exponential function the parent graph(no transformations) has a horizontal asymptote at y=0. The graph approaches this asymptote and does not go below it. So the RANGE is (0,Infinity) but this can change as the transformations of the graph may shift the graph and asymptote vertically. This will obviously depend on the problem you are working on.
but for example: if y= 3/(1+2e^(-5x) ), how can i determine the domain of this equation without looking the graph??
monika piseth Ahhh that is a rational expression with a exponential denominator. When dealing with Rational expressions your domain will be all real numbers except for the values where the denominator is equal to zero. So you will want to the equation in the denominator equal to zero and solve for x. That value will be the x value of your vertical asymptote and not apart of your solution.
Why x is not subtracted by 2
I really need help graphing f(x)= -3+e^x
Wait, I am confused. Why is 2e^x the parent function? Isn't the 2 that's being multiplied a transformation?
yes e^x is the parent function, I guess I meant to say the function without horizontal or vertical shifts
Thank you professor!
..2018
but if it's at plus 4 should'nt it be at 5 cuz originally y was 1?
"asymtoPe"
THANK YOU SO MUCH!!! I have been stuck on this for hours.
In the video 2:26 u wrote x= 1 but it would be 0 as u said Sir
you're the best prof. McLogan
my precal teac wants the smae but not by plotting points so ihave to do it by memory. or use the 1/e factors?
i have this case:
e^x-3x and i need to find the roots, how can i do that?
all i can think of is just e^x=3x and have a symmetry between the graphs of functions e^x and a 3x?
Hi mr mclogan, can I confirm if it is possible for y=0 or does it give me (N.A)? I know that y=0 is the asymptote but I’m not too sure how asymptotes work
And if I have something like y=e^x, no matter how I modify the x (eg. y=e^2x, y=e^-1/2x) the graph will always remain the same shape?
dude is there a way to do it without calculator? In my IB Math course we are not allowed to use calculators for these kind of questions
yes, just use transformation and the parent graph, at the end of the video are more examples
his students are so lucky to have him as their teacher
thanks , mister
this was awesome
The one thing I don’t understand is why Y equals 1 when X is 0 . I can’t wrap my head around it cause when you do the math 0-2 =-2 so it’s be 2e^-2+4 which isn’t 1 ... what am I missing?
x^0 is 1 since x represents any number, however the y-intercept changes based on the transformations
Oh, I see thanks a lot!
The first video that actually explains how to do this
happy to be able to help
Oh okay Sir, asymtote does not change? Remains at y=0
no the asymptote moves up 4 because that is the vertical shift.
Free Math Videos Absolutely, however the 2 in front of the e does not effect it, because of course 2 x 0 is 0, HOWEVER the further transformation moves it up to 4. Thank you very much, watch your videos from the UK, city of Bristol.
thank you have bn struggling to get correct answers waal thank u
you are very welcome! happy to help
man this is one tough subject to explain
how does the negative to in the exponent affects the graph?
roberto sicairos reflect over the y-axis
It is going to go up and down like sine or cosine exponentially. Values between 0 and 1 is decaying instead of increasing. Values between 0 and -1 is like cosine or sine decaying.
Fantastic sir
happy to help
You are confused your own self Sir! :D I feel bad for the students you teach lol
I make a lot of videos, yes sometimes I will trip myself up, no worries, I correct mistakes or make sure I provide another example to make sure students understand
Muhammad Fayaz Yourish he’s actually really helpful. He’s also human. Everyone makes mistakes
You made a ton of mistakes lel
Not unusual, I make my videos real time, always struggled with making mistakes when I took math, they still happen, I am human, I try to correct any and all mistakes, I discover by myself or by others, Let me know where I went wrong and I will definitely correct it.
It's alright, I still follow your videos. I like your way of teaching!
well thank you and I do appreciate you letting me know when I make mistakes, please if you notice anything, let me know. I do not want to confuse anyone
Karrar Aldubaissi y
Brian McLogan cuÿtdssryjx