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# C3 transformations of functions- question help.

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1. Hi,

I've been doing a question from the textbook and I don't really understand why the answer is what it is. It gives the equation of a circle as x^2 +y^2 =1. Then it says it is stretched sf3 parallel to x axis and sf2 parallel to y axis. You have to write the new equation.

I though it would be (x/3)^2 + (2y)^2 =1 leading to (x^2/9)+ (4y^2)=1 but it's given as (x^2/9) + (y^2/4)= 1. I don't really understand the 'y' bit. Please could someone explain.

Thanks
2. You have replaced y with 2y for the stretch SF 2 parallel to y axis when you should have replaced y with y/2 just as you replaced x with x/3. Why did you treat y and x differently when applying the transformations?
3. (Original post by VioletPhillippo)
Hi,

I've been doing a question from the textbook and I don't really understand why the answer is what it is. It gives the equation of a circle as x^2 +y^2 =1. Then it says it is stretched sf3 parallel to x axis and sf2 parallel to y axis. You have to write the new equation.

I though it would be (x/3)^2 + (2y)^2 =1 leading to (x^2/9)+ (4y^2)=1 but it's given as (x^2/9) + (y^2/4)= 1. I don't really understand the 'y' bit. Please could someone explain.

Thanks
If you've been taught that "You do the opposite for x only" then you've been taught wrong. You do the same throughout.

Take where a line with some gradient passes through . You are literally translating the line onto that point by doing so. By your logic it would be which translates it onto the wrong co-ordinate of
4. The reason why your teachers say "you do the opposite for x only" is because you generally have an equation of the form , then it's true that to stretch it by a factor of you do .

But note that that is the same thing as which is what you're really doing. So in the case when it's not as clear cut as then you need to remember that stretching in the y direction really means .

So that's why for you do
5. (Original post by Zacken)
The reason why your teachers say "you do the opposite for x only" is because you generally have an equation of the form , then it's true that to stretch it by a factor of you do .

But note that that is the same thing as which is what you're really doing. So in the case when it's not as clear cut as then you need to remember that stretching in the y direction really means .

So that's why for you do
Thanks, that's a really clear explanation
6. (Original post by VioletPhillippo)
Thanks, that's a really clear explanation
Great!

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