maths adv - transformations question (1 Viewer)

[toaster1822]

Just a bit lost on the order of transformations for a graph.
I used to think it was just going left to right in the form f(x) = a(b(x+c))+d, but I've heard conflicting other methods such as:
Horizontal translation
Horizontal dilation/reflection
Vertical translation
Vertical dilation/reflection
and various other ways.

Is there a 'standard' method, or are they all valid?

 

[Trial&Error]

There's multiple ways to do it, but here's normally how what I do:

1)fully factorise the function so the coefficient of x is 1: y=af(b(x−c))+d

then use BODMAS

2)start with horizontal transformations which are inside the brackets in the order:
a)Horizontal dialation / reflection by a factor of "1/b"
b)Horizontal shift by "c"

3) repeat the same with vertical transformations in the order:
a)vertical dialation / reflection by a factor of "a"
b)vertical shift by "d"

I hope this helps

 

[toaster1822]

Thanks for the quick reply. I'll stick with your method then, seems logical.

 

[coolcat6778]

Thanks for the quick reply. I'll stick with your method then, seems logical.

It is indeed the most logical and systematic way.
Now try this question

 

[toaster1822]

so f(2(x-1/2))
so it starts with a horizontal dilation by 1/2, then a horizontal translation 1/2 to the right.
So would the answer be C?