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# Maths C3 - Drawing Inverse Exponential Function graphs.. Help? watch

1. So yet again I'm struggling to self-teach Maths...

I find the Edexcel C3 Modular Maths Textbook difficult to learn from which ends up leaving gaps in my knowledge of the subject.

How would you go about drawing Inverse Exponential Functions onto a graph?
The example I'm struggling with atm is...

I know that this is the Inverse of y=e^(-x+3) but I am still having trouble drawing it without having to draw the non-inverse exponential function first!!
2. (Original post by Philip-flop)
So yet again I'm struggling to self-teach Maths...

I find the Edexcel C3 Modular Maths Textbook difficult to learn from which ends up leaving gaps in my knowledge of the subject.

How would you go about drawing Inverse Exponential Functions onto a graph?
The example I'm struggling with atm is...

I know that this is the Inverse of but I am still having trouble drawing it without having to draw the non-inverse exponential function first!!
Seems easier just to draw ln(3-x) instead of finding the inverse and reflecting it, no?
3. (Original post by Philip-flop)
So yet again I'm struggling to self-teach Maths...

I find the Edexcel C3 Modular Maths Textbook difficult to learn from which ends up leaving gaps in my knowledge of the subject.

How would you go about drawing Inverse Exponential Functions onto a graph?
The example I'm struggling with atm is...

I know that this is the Inverse of but I am still having trouble drawing it without having to draw the non-inverse exponential function first!!
Consider the graph of and apply transformations.
4. log(0.000000001) = a very negative number
log(1) = 0
as a tends to infinity log(a) tends to infinity and the derivative of log(a) tends to 0

you can sketch log(x) using those four facts, then apply a couple of transformations
5. (Original post by SeanFM)
Seems easier just to draw ln(3-x) instead of finding the inverse and reflecting it, no?
Yeah that's what I want to be able to do. But the book doesn't really explain how to achieve this
(Original post by NotNotBatman)
Consider the graph of and apply transformations.
Yeah but I don't really understand how to draw Natural Log graphs in the first place
6. (Original post by Philip-flop)
Yeah that's what I want to be able to do. But the book doesn't really explain how to achieve this

Yeah but I don't really understand how to draw Natural Log graphs in the first place
As transformations go I think at A-level ln(3-x) is probably one of the most difficult ones I think.

You just have to start with lnx (you should become familiar with it) and then apply transformations.

Also in general with any graphs, if you know/can guess the shape then all you need are some points and you're set.

Eg thinking of ln(3-x) as a function.. what's the domain? You also know that ln(...) = 0 at some point, so what point is that at? What happens when x is very large (positive/negative? only one of those is in the range though) you can ask these kind of questions for any graph.
7. Would I be right in thinking that if... f(x) = lnx then f(-x+3) = ln(-x+3) ?? <<< also written as ln(3-x)
So I could just make my transformations that way?
8. (Original post by Philip-flop)
Yeah that's what I want to be able to do. But the book doesn't really explain how to achieve this

Yeah but I don't really understand how to draw Natural Log graphs in the first place
Do you know the graph of ? As is it's inverse, it's a reflection in the line y=x. It should be in the textbook, or you can use an online grapher like desmos.
9. (Original post by NotNotBatman)
Do you know the graph of ? As is it's inverse, it's a reflection in the line y=x. It should be in the textbook, or you can use an online grapher like desmos.
Yes I know that e^x and that ln(x) is it's inverse. But for some reason I'm still having trouble

I have been using Desmos to try and make more sense of it
10. (Original post by Philip-flop)
Would I be right in thinking that if... f(x) = lnx then f(-x+3) = ln(-x+3) ?? <<< also written as ln(3-x)
So I could just make my transformations that way?
Yes.
11. (Original post by Philip-flop)
Would I be right in thinking that if... f(x) = lnx then f(-x+3) = ln(-x+3) ?? <<< also written as ln(3-x)
So I could just make my transformations that way?
Exactly.
12. To get from to we first translate the curve by vector . Can you work out what we do next to get to ?
13. Wonderful explanations everyone!! I think I'm finally starting to understand it
14. For anyone who is interested. Here is my answer...
15. The only thing I have trouble with now is working out where Natural Log graphs cross the x-axis say for example...

16. (Original post by Philip-flop)
The only thing I have trouble with now is working out where Natural Log graphs cross the x-axis say for example...

They cross the x axis when y=0
in this case
ln(2x) +3 = 0
ln(2x)=-3
2x=e^-3
x=(e^-3)/2
17. (Original post by ValerieKR)
They cross the x axis when y=0
in this case
ln(2x) +3 = 0
ln(2x)=-3
2x=e^-3
x=(e^-3)/2
Thank you so much!! I had actually forgotten how to solve Logs for a second there! You helped a lot!!
18. (Original post by Philip-flop)
So yet again I'm struggling to self-teach Maths...

I find the Edexcel C3 Modular Maths Textbook difficult to learn from which ends up leaving gaps in my knowledge of the subject.

How would you go about drawing Inverse Exponential Functions onto a graph?
The example I'm struggling with atm is...

I know that this is the Inverse of y=e^(-x+3) but I am still having trouble drawing it without having to draw the non-inverse exponential function first!!
As a side question, you might want to double check your inverse function.

Your original function () crosses the x-axis at .

Your inverse should then cross the y-axis at , however, your inverse crosses the y-axis at .
19. (Original post by simon0)
As a side question, you might want to double check your inverse function.

Your original function () crosses the x-axis at .

Your inverse should then cross the y-axis at , however, your inverse crosses the y-axis at .
No, in this case ln(3-x) is the inverse of an e^x graph. I wasn't trying to find the reverse of ln(3-x) I was trying to work out what ln(3-x) looks like on a graph.

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