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# Graph transformation

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1. What is the graph transformation f(1-x)? I'm trying to graph f(x)=2ln(1-x), and I got stretch in y axis factor 2, shift left 1 unit and reflect in y axis. However, the answers say it is a shift right one unit. I checked on an online graph maker and they also show a shift right. Can anyone explain why the 1 causes a shift to the right and not the left? I thought it had something to do with the fact it has been reflected but was not sure...
2. Actually I thought about it, I think it depends on the order in which you do the transformations.... Does anyone know what the correct order of doing transformations is? Like how we learn BODMAS, is there a kind of sequence that can be used to correctly do graph transformations?
3. (Original post by Uni12345678)
What is the graph transformation f(1-x)? I'm trying to graph f(x)=2ln(1-x), and I got stretch in y axis factor 2, shift left 1 unit and reflect in y axis. However, the answers say it is a shift right one unit. I checked on an online graph maker and they also show a shift right. Can anyone explain why the 1 causes a shift to the right and not the left? I thought it had something to do with the fact it has been reflected but was not sure...
Depends on the order, but there is no stretch in from

Firstly it would be reflected in x=0 (the y-axis) -

Then it would be shifted by vector [1,0] -
4. (Original post by RDKGames)
Depends on the order, but there is no stretch in from

Firstly it would be reflected in x=0 (the y-axis) -

Then it would be shifted by vector [1,0] -
Oh thank you! I get it! So when considering a transformation that involves moving along the x axis, the form must be including a positive x value as you have shown, yes?
5. (Original post by Uni12345678)
Oh thank you! I get it! So when considering a transformation that involves moving along the x axis, the form must be including a positive x value as you have shown, yes?
What do you mean?

Translating by vector [a,b] would make it
6. (Original post by RDKGames)
What do you mean?

Translating by vector [a,0] would make it
So when we learn the rules like f(x-1) is shift to right etc... The x must be positive for the transformation to be valid; if x is negative we can't just reflect and then move by 1 unit to the right because of -1, it must be to the right because the x is negative so we factorise to change it to. Positive by taking out negative 1 and that would make the transformation go to the left as it would create a positive 1...

Okay it makes sense to me, I'm sorry it's complicated ahhaha
7. For transforming to there are always two different sets of transformations.
The first is a translation by vector followed by a stretch parallel to the x axis SF 1/a.
It is also a stretch parallel to x axis SF 1/a followed by a translation by vector .
These are the only order they can be in. Of course if a is negative then there will be a reflection in the y axis.
8. (Original post by Uni12345678)
So when we learn the rules like f(x-1) is shift to right etc... The x must be positive for the transformation to be valid; if x is negative we can't just reflect and then move by 1 unit to the right because of -1, it must be to the right because the x is negative so we factorise to change it to. Positive by taking out negative 1 and that would make the transformation go to the left as it would create a positive 1...

Okay it makes sense to me, I'm sorry it's complicated ahhaha
The best advice I can give you is to put brackets around the x, and do any transformations concerning it inside that bracket. I will redo the first example with brackets to clear up any confusion and hopefully make it clearer:

Reflection in the y-axis:

Translate by vector [1,0]:

Then for the banter we can choose to translate it by another vector [-8,0]:

And then stretch it in along the x-axis by scale factor 1/2:
9. (Original post by RDKGames)
The best advice I can give you is to put brackets around the x, and do any transformations concerning it inside that bracket. I will redo the first example with brackets to clear up any confusion and hopefully make it clearer:

Reflection in the y-axis:

Translate by vector [1,0]:

Then for the banter we can choose to translate it by another vector [-8,0]:

And then stretch it in along the x-axis by scale factor 1/2:
Thank you! You've been very helpful, also your banter is brilliant 😂

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