Order of graph transformations Watch

ilovemath
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#1
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#1
If I am given a graph and asked to do multiple transformations, would the following order ALWAYS give me the correct answer?


- Left/right translation
- Stretch/shrink
- Reflect
- Up/down translation


If not then could someone please give me an order that would?
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elldeegee
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#2
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From the various sketches i have just done, yes it seems to always work.

But surely if you are told to do multiple transformations, then you would be told what transformaions? If so i would recommend just do it in the order they say, that way you won't miss one of the transformations out.
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gdunne42
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#3
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(Original post by ilovemath)
If I am given a graph and asked to do multiple transformations, would the following order ALWAYS give me the correct answer?


- Left/right translation
- Stretch/shrink
- Reflect
- Up/down translation


If not then could someone please give me an order that would?
1. stretch/reflect doesn't matter
then
2. translations

try f(2x - 1) on a curve that crosses (0,0) and a max at (4,6)

try them in different orders

(BIDMAS)
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ttoby
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(Original post by gdunne42)
1. stretch/reflect doesn't matter
then
2. translations

try f(2x - 1) on a curve that crosses (0,0) and a max at (4,6)

try them in different orders

(BIDMAS)
Something like that is quite tricky and easy to get wrong. What I would do is to do it in stages:

Start with f(x), transform to f(x+1) where we're replacing x with x+1, then transform to f(2x+1) where we're replacing x with 2x.

If you tried to do it in the other order then you would start with f(x), then get f(2x) then to go to f(2x+1) it's not clear what we're replacing x, with so perhaps it's better to use the first order we tried.
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dgshsjzngs
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#5
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It's simple, always follow:

1. Translation in x
2. Stretch in x
3. Reflect in x
4. Reflect in y
5. Stretch in y
6. Translate in y
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Zacken
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#6
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(Original post by ttoby)
Something like that is quite tricky and easy to get wrong. What I would do is to do it in stages:

Start with f(x), transform to f(x+1) where we're replacing x with x+1, then transform to f(2x+1) where we're replacing x with 2x.

If you tried to do it in the other order then you would start with f(x), then get f(2x) then to go to f(2x+1) it's not clear what we're replacing x, with so perhaps it's better to use the first order we tried.
For f(2x) \mapsto f(2x+1) we need only do x \mapsto x+ \frac{1}{2}
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harryleavey
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If it is just and x stretch and a y stretch then order does not matter
If it is just and x transformation and a y translation then order does not matter
If it is an x transformation and an x stretch then the transformation is first
If it is a y transformation and a y stretch then stretch is first
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pixel1232541345
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#8
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#8
(Original post by dgshsjzngs)
It's simple, always follow

1. Translation in x
2. Stretch in x
3. Reflect in x
4. Reflect in y
5. Stretch in y
6. Translate in y
Doesn't seem to work, e.g. trying your algorithm on the following two identical functions

y=1/(0.5x+1)+3 (1)

and

y = 2/(x+2)+3 (2)

gives conflicting results. E.g. (1) transforms (1,1) to (0,4) whereas (2) transforms (1,1) to (-1,5)...
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BTAnonymous
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#9
(Original post by pixel1232541345)
Doesn't seem to work, e.g. trying your algorithm on the following two identical functions

y=1/(0.5x+1)+3 (1)

and

y = 2/(x+2)+3 (2)

gives conflicting results. E.g. (1) transforms (1,1) to (0,4) whereas (2) transforms (1,1) to (-1,5)...
they are the same result...
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