How do you find the asymptotes after a combination of transformations?

Apply the transformations to the asymptotes one at a time , in the same order as you apply them to the graph. An asymptote is just a line, so each stage moves or stretches it in exactly the way that stage moves or stretches the curve.

A LevelMathsCambridge (CIE)Pure 1FlashcardsAlgebra & FunctionsCombinations of Transformations

Combinations of Transformations (Cambridge (CIE) A Level Maths: Pure 1): Flashcards

Exam code: 9709

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FrontCombinations of Transformations
In $y = k f (a x + b) + c$ , which transformation is applied first?

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Cards in this collection (5)

In $y = k f (a x + b) + c$ , which transformation is applied first?
The horizontal one, inside the brackets.
The vertical transformations, which sit outside the brackets, are applied afterwards.
When two vertical transformations act outside the brackets, which goes first?
The stretch or reflection goes first, and the translation afterwards.
In $y = 3 f (x) - 2$ that means stretching by scale factor $3$ and only then translating down by $2$ .
True or False?
$y = 3 f (x) - 2$ and $y = 3 (f (x) - 2)$ describe the same graph.
False.
The second expands to $y = 3 f (x) - 6$ , which is a different graph.
Translating before stretching means the stretch acts on the shift as well, which is exactly why the order is fixed.
The point $(- 2, 6)$ lies on $y = f (x)$ . Where does it move to on $y = 3 f (x) - 2$ ?
It moves to $(- 2, 16)$ .
The stretch takes the $y$ -coordinate to $3 \times 6 = 18$ and the translation then brings it down to $16$ , while the $x$ -coordinate is untouched because both transformations are vertical.
How do you find the asymptotes after a combination of transformations?
Apply the transformations to the asymptotes one at a time, in the same order as you apply them to the graph.
An asymptote is just a line, so each stage moves or stretches it in exactly the way that stage moves or stretches the curve.

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