Transformations

username2391335

4

For maths when you do transformations do you do translations or stretches first?

Original post by spacenerd98

For maths when you do transformations do you do translations or stretches first?

Neither, pick whichever you want first. Transformations don't have a BIDMAS type hierarchy of operations.

Reply 2

username2391335

OP

4

Original post by RDKGames

Neither, pick whichever you want first. Transformations don't have a BIDMAS type hierarchy of operations.

Thank you x

Reply 3

B_9710

18

Original post by spacenerd98

Thank you x

In what context do you mean when you ask this question? Can you give any examples?

Reply 4

username2391335

OP

4

Original post by B_9710

In what context do you mean when you ask this question? Can you give any examples?

So i did a question and it was like y=x to y=2x-2 and the mark scheme said that if you did the stretch first then the translation would only be across by one not two? idk if I'm being stupid but why does it matter which order its in

Original post by spacenerd98

So i did a question and it was like y=x to y=2x-2 and the mark scheme said that if you did the stretch first then the translation would only be across by one not two? idk if I'm being stupid but why does it matter which order its in

Oh, in terms of functions then the order sort of matters whereas geometrically it doesn't.

Transformation

x \mapsto 2x-2

would involves either:

1. Stretch in the x-axis by a scale factor of

\frac{1}{2}

to give

y=2x

followed by translation by vector

[1,0]

which gives

y=2(x-1)=2x-2

as required.

2. A translation by vector

[2,0]

which gives

y=x-2

and then a stretch by a scale factor of

\frac{1}{2}

along the x-axis giving you

y=2x-2

So really, the ORDER doesn't matter, but the specifics of each transformation step depend on the order you choose.

The reason for the order specifics being different is because every change you make affects the variable directly and not the entire LHS of the equation as a whole. For example, it wouldn't be right if you went went from

y=2x

with a translation of

(2,0)

and say that the answer is

y=2x-2

because you need to apply this change directly to the variable, giving you

y=2(x-2)=2x-4

instead.

Perhaps a teacher on here can explain it more clearly, for some reason I struggle to explain this properly. @notnek

(edited 7 years ago)

Reply 6

Notnek

21

Original post by spacenerd98

So i did a question and it was like y=x to y=2x-2 and the mark scheme said that if you did the stretch first then the translation would only be across by one not two? idk if I'm being stupid but why does it matter which order its in

Order can matter. E.g. let's start with y = x and do a translation by 1 unit to the left i.e. f(x)->f(x+1) followed by a stretch by 1/2 in the x-direction i.e. f(x)->f(2x).

y = x

f(x) -> f(x+1) : y = x + 1

f(x) -> f(2x) : y = 2x + 1

Now the other way around:

y = x

f(x) -> f(2x) : y = 2x

f(x) -> f(x+1) : y = 2(x+1) = 2x + 2

So you end up with something different.

If you wanted to get y = 2x + 1 instead of y = 2x + 2 you would need to use f(x)->f(x+1/2) instead here. Does that make sense?

In general, order matters when you have two or more horizontally oriented transformations. Similarly order matters when you have two or more vertically oriented transformation. But vertical transformations do not affect horizontal transformations and vice-versa.

It's not important for you to remember this but it is important that you understand that order can matter.

(edited 7 years ago)

Transformations

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