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C3 Transformations Maths Question - HELP watch

1. I am currently revising transformations and seem to be getting confused.
Every question I encounter I use these rules;

y = f(x-a) + b ----> Translation [a, b]
y = f( -x) ------> Reflection in y-axis
y = - f(x) -----> Reflection in x-axis
y = f ( x/a) -----> Stretch in x-axis by a
y = a f (x) ---> Stretch in y-axis by a

I sometimes bring everything affecting the y to the other side and that makes it easier.
Anyways the question I don't understand is....;

"Describe geometrically how the curve y = 1 + sinx is transformed into y = 1 - sinx" - The answer at the back of the book is reflection in y-axis.

When I do it;
y = 1 - sinx
y - 1 = -sinx
-(y -1) = sinx >> Reflection in x-axis??
I don't understand how it is a reflection in the y-axis?
Does anyone have any techniques to approaching a question - I need to nail ANY transformation question

HELP
2. (Original post by Pumuki63)
I am currently revising transformations and seem to be getting confused.
Every question I encounter I use these rules;

y = f(x-a) + b ----> Translation [a, b]
y = f( -x) ------> Reflection in y-axis
y = - f(x) -----> Reflection in x-axis
y = f ( x/a) -----> Stretch in x-axis by a
y = a f (x) ---> Stretch in y-axis by a

I sometimes bring everything affecting the y to the other side and that makes it easier.
Anyways the question I don't understand is....;

"Describe geometrically how the curve y = 1 + sinx is transformed into y = 1 - sinx" - The answer at the back of the book is reflection in y-axis.

When I do it;
y = 1 - sinx
y - 1 = -sinx
-(y -1) = sinx >> Reflection in x-axis??
I don't understand how it is a reflection in the y-axis?
Does anyone have any techniques to approaching a question - I need to nail ANY transformation question

HELP
are you from abroad or the UK?
3. (Original post by TeeEm)
are you from abroad or the UK?
UK, why?
4. (Original post by Pumuki63)
I am currently revising transformations and seem to be getting confused.
Every question I encounter I use these rules;

y = f(x-a) + b ----> Translation [a, b]
y = f( -x) ------> Reflection in y-axis
y = - f(x) -----> Reflection in x-axis
y = f ( x/a) -----> Stretch in x-axis by a
y = a f (x) ---> Stretch in y-axis by a

I sometimes bring everything affecting the y to the other side and that makes it easier.
Anyways the question I don't understand is....;

"Describe geometrically how the curve y = 1 + sinx is transformed into y = 1 - sinx" - The answer at the back of the book is reflection in y-axis.

When I do it;
y = 1 - sinx
y - 1 = -sinx
-(y -1) = sinx >> Reflection in x-axis??
I don't understand how it is a reflection in the y-axis?
Does anyone have any techniques to approaching a question - I need to nail ANY transformation question

HELP
This uses the fact that -sinx = sin(-x)

For this to be a reflection in the x-axis you would need y = -(1+sinx) = -1-sinx
5. (Original post by Pumuki63)
UK, why?
nothing to worry
it is just the way you are attempting this, reminds me of approaches taught abroad...
6. (Original post by TenOfThem)
This uses the fact that -sinx = sin(-x)

For this to be a reflection in the x-axis you would need y = -(1+sinx) = -1-sinx
Yes I've heard about that: -sinx = sin -x, is that just because it's an odd function? Does is then work with tanx as well? and when do you know to do that/or is it always?

I get what you mean with "y = -(1+sinx) = -1-sinx" so does that mean the answer in the book is wrong?
7. (Original post by TeeEm)
nothing to worry
it is just the way you are attempting this, reminds me of approaches taught abroad...
Are you from UK? Do you know any other approach that may be easier? At the minute I'm just learning it independently and trying to master transformations (since I always lose some marks in these questions) and my teacher isn't............ very "effective" shall we say?
8. (Original post by Pumuki63)
Yes I've heard about that: -sinx = sin -x, is that just because it's an odd function? Does is then work with tanx as well? and when do you know to do that/or is it always?

I get what you mean with "y = -(1+sinx) = -1-sinx" so does that mean the answer in the book is wrong?
No the book is correct

y = 1 - sinx = 1 + sin(-x) = f(-x) so a reflection in the y-axis
9. (Original post by Pumuki63)
Are you from UK? Do you know any other approach that may be easier? At the minute I'm just learning it independently and trying to master transformations (since I always lose some marks in these questions) and my teacher isn't............ very "effective" shall we say?
do not worry ... you may be too conscientious
this is genuinely a hard question.

This transformation is very hard to see.

I have 9 Year 13 students this year with varying AS UMS from 263 to 295.

practically all of them will get A* but I think NONE of them would have seen this ...

10. (Original post by TenOfThem)
No the book is correct

y = 1 - sinx = 1 + sin(-x) = f(-x) so a reflection in the y-axis
Ok that makes sense Thank you!!!
So is f(-x) always = -f(x) in odd functions??
Because in e.g. y = -x^2, is not the same as (-x)^2?
11. (Original post by Pumuki63)
Ok that makes sense Thank you!!!
So is f(-x) always = -f(x) in odd functions??
Because in e.g. y = -x^2, is not the same as (-x)^2?
Yes, in odd functions - not in even functions
12. (Original post by TeeEm)
do not worry ... you may be too conscientious
this is genuinely a hard question.

This transformation is very hard to see.

I have 9 Year 13 students this year with varying AS UMS from 263 to 295.

practically all of them will get A* but I think NONE of them would have seen this ...

It's reassuring to know it's a difficult question, I am aiming for an A* so I want to nail any transformation question I can find but this one put me off...
At the minute I am thinking (thanks to TenOfThem) that I have to use what he/she suggested -f(x) = f(-x) but then if I use that in other questions I find it doesn't always work - don't know if it's just me that's doing the question wrong (I figured it only works with odd functions - so do I just use it for odd functions).
13. (Original post by TenOfThem)
Yes, in odd functions - not in even functions
So should it work with ALL odd functions ?? if i make that conclusion?
because I find it doesn't always work (may be me working it out wrong)?
And then when it's an odd function such as tanx, if it's -tanx, that is equal to tan(-x) so when do I know whether it's reflection in x or y-axis (or is it both)?
14. (Original post by Pumuki63)
It's reassuring to know it's a difficult question, I am aiming for an A* so I want to nail any transformation question I can find but this one put me off...
At the minute I am thinking (thanks to TenOfThem) that I have to use what he/she suggested -f(x) = f(-x) but then if I use that in other questions I find it doesn't always work - don't know if it's just me that's doing the question wrong (I figured it only works with odd functions - so do I just use it for odd functions).
unfortunately this is true (use of odd functions)

but I have never seen a question like this in any recent exam.
15. (Original post by TeeEm)
unfortunately this is true (use of odd functions)

but I have never seen a question like this in any recent exam.
I'm doing AQA and there's none like these in past papers either but there is in the textbook so I think my best bet is to try to understand it in case (you never know what they're going to throw at you the next year)
16. (Original post by Pumuki63)
I'm doing AQA and there's none like these in past papers either but there is in the textbook so I think my best bet is to try to understand it in case (you never know what they're going to throw at you the next year)
I do not think Odd/even functions are taught at current AQA syllabus, but it does not hurt to know...
17. (Original post by TeeEm)
I do not think Odd/even functions are taught at current AQA syllabus, but it does not hurt to know...
Oh ok, so do I not need to know about that transformation in AQA (odd and even functions)?
18. (Original post by Pumuki63)
Oh ok, so do I not need to know about that transformation in AQA (odd and even functions)?
I last time I taught AQA students were in 2011 - 2013 and that was not part of their course.
I do not think the Syllabus has changed.

only board that does this topic, at standard A level, is MEI
19. (Original post by TeeEm)
I last time I taught AQA students were in 2011 - 2013 and that was not part of their course.
I do not think the Syllabus has changed.

only board that does this topic, at standard A level, is MEI
Ok thank you for the info, I think I'm going to just leave it, I understand it-ish at least.
Can I ask another question, cosecx --> cosec(2x +30)
I would do cosec(2(x +15)), does it matter which way round it is?
stretch in x-direction by 1/2 and translation [-15, 0]
OR
translation [-15, 0] and stretch in x-direction by 1/2

Are they both correct???
20. (Original post by Pumuki63)
Ok thank you for the info, I think I'm going to just leave it, I understand it-ish at least.
Can I ask another question, cosecx --> cosec(2x +30)
I would do cosec(2(x +15)), does it matter which way round it is?
stretch in x-direction by 1/2 and translation [-15, 0]
OR
translation [-30, 0] and stretch in x-direction by 1/2

Are they both correct???
almost both correct

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