Outside the brackets, which comes first, a stretch or a translation?

The stretch (or reflection) comes first, and the translation afterwards. That is the opposite way round from inside the brackets, which is exactly what makes the order easy to get wrong.

True or False? Applying a stretch and a translation in either order gives the same graph.

False. Stretching and then translating lands the graph somewhere different from translating and then stretching, because the stretch also scales any translation already applied.

How are asymptotes handled in a combination of transformations?

They are transformed too, one step at a time and in the same order as the graph itself. A sketch of the transformed graph should show the transformed asymptotes.

When you sketch a transformed graph, what should you mark on it?

The new coordinates of any points that were marked on the original graph. Where the equation makes it possible, also give the points where the transformed graph crosses the axes.

A LevelMathsEdexcelPureFlashcardsAlgebra & FunctionsCombinations of Transformations

Combinations of Transformations (Edexcel A Level Maths: Pure): Flashcards

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FrontCombinations of Transformations
In what order do you apply a combination of graph transformations?

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Cards in this collection (6)

In what order do you apply a combination of graph transformations?
Horizontal ones first, from inside the brackets, then vertical ones from outside.
In $y = k f (a x + b) + c$ , the $a$ and $b$ act first and the $k$ and $c$ afterwards.
Inside the brackets, apply $______$ before stretches and reflections.
Inside the brackets, apply translations before stretches and reflections.
So in $f (a x + b)$ the $+ b$ is dealt with before the $\times a$ .
Outside the brackets, which comes first, a stretch or a translation?
The stretch (or reflection) comes first, and the translation afterwards.
That is the opposite way round from inside the brackets, which is exactly what makes the order easy to get wrong.
True or False?
Applying a stretch and a translation in either order gives the same graph.
False.
Stretching and then translating lands the graph somewhere different from translating and then stretching, because the stretch also scales any translation already applied.
How are asymptotes handled in a combination of transformations?
They are transformed too, one step at a time and in the same order as the graph itself.
A sketch of the transformed graph should show the transformed asymptotes.
When you sketch a transformed graph, what should you mark on it?
The new coordinates of any points that were marked on the original graph.
Where the equation makes it possible, also give the points where the transformed graph crosses the axes.

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