Order of transforming a function

[dragon513]

Q. y= f(-x-4)

Hi, I was wondering why I must factor out -1 to make the function y=(-1(x+4)).
I tried to look in the texbook but it doesn't say why I have to do it that way..

Also when transforming a fuction, why should I do it from left to right?
y=a(f(x-b))+d
Isn't it more logical to do what's in the bracket first?

Thank you.

 

[HallsofIvy]

Q. y= f(-x-4)
Hi, I was wondering why I must factor out -1 to make the function y=(-1(x+4)).
I tried to look in the texbook but it doesn't say why I have to do it that way..

If you specifically mean that f(x)= 1/x you should say so at the start!
If f(x)= 1/x then f(-x-4)=1/(-x-4) of course. You don't HAVE to write that as 1/(-(x+4))= -1/(x+4) but it is a lot simpler to write and work with that way.

Also when transforming a fuction, why should I do it from left to right?
y=a(f(x-b))+d
Isn't it more logical to do what's in the bracket first?
Thank you.

And what, exactly, is in the bracket? f(x-b)? Since you haven't told us what f is, I don't know HOW to do that. Exactly WHAT do you mean by
y= a(f(x-b))+ d?