# Order of graph transformations

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?
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.
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)
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.
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
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 $x \mapsto x+ \frac{1}{2}$
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
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)...
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...