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.

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.

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?

- 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)

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)

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.

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

1. Translation in x

2. Stretch in x

3. Reflect in x

4. Reflect in y

5. Stretch in y

6. Translate in y

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.

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 $x \mapsto x+ \frac{1}{2}$

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

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

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

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)...

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)...

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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