When transforming a graph, does it matter which order you list the transformations?

i think it would be

1) enlargement sf 1/3 along x axis
2) translation (-2, 0)
3) enlargement sf 5 along y axis

It defo matters what order you put it

Alright, thankyou.
But then, how do i decide which goes first?

I.e. Say if it asks Describe the geometrical transformation to take y=cosx to y=5cos(x+3)


And what would the transformation be with something a little more difficult like
Y=cosx to y=5cos(3x+2)
Thanks guys

Any linear transformation of $y=\mathrm{f}(x)$ can be written as

$y=d(\mathrm{f}(b(x+a))+c)$

The order is a,b,c,d.

The curve is shifted 'a' along. If a>0 then it's to the left. If a<0 then it's to the right.

The curve is then 'squeezed' in the x-direction by a factor of b (or if 0<b<1, stretched). If b is negative, consider what happens if it is positive, then flip everything in the y-axis.

The curve is then moved up or down by an amount 'c'.

Finally the curve is squeezed or stretched in the y-direction by a factor of d.

Ah man, thankyou. Looking at it the way you presented is easy. So just to recap it makes aboslutely NO difference in which order the transformations are applied, EVER?

And what about the stuff they are saying on this page, then? Are they incorrect?
http://www.thestudentroom.co.uk/showthread.php?t=1662123&page=6
BTW i MUCH apreciate your help man

Horizontal transformations and vertical transformations do not affect each other. Thus the only problematic questions are those with $f(ax+b)$ and $af(x) + b$. In these cases, the graph is first stretched and then translated.

Horizontal transformations and vertical transformations do not affect each other. Thus the only problematic questions are those with $f(ax+b)$ and $af(x) + b$. In these cases, the graph is first stretched and then translated.

Guys, there is SO many conflicting views here.
Seriously, does anybody KNOW the answer?

Some of the stuff here is correct, some of it is wrong. The only post I agree with entirely (apart from my own) is post 2.

Take a look at this example:

y= c*f(bx+a)+d

For this, you do the following;

Start with f(x)
Translate by -a in the x direction
Stretch by factor 1/b in the x direction
Stretch by factor c in the y direction
Translate by d in the y direction

There is a certain amount of room for changing the order here (depending on what you're changing), but I won't go through that as it will confuse you. Just learn it in this order.

Why have you got translate before stretch once, and stretch before translate for the second set? I would have done it the other way (stretch, translate, stretch, translate) as that actually follows some kind of ruling that makes sense.

I guess it would depend on whether it's bx + a or b(x+a)?