Order For Transformations / Translations?

Apr 2016
12
0
Connecticut
Hello,

I am struggling with doing transformations and translations of the graphs of functions. Specifically I don't understand the order I am supposed to do them in. I have had to do problems where I am given the graph of a function and then I am asked to select the correct new graph based on the given translations and transformations.

For instance if I have g(x) = -f(x-2) -4

I believe I have to do the following

*A reflection over the x-axis because of -f(x)
*shift right two units because of (x-2)
*shift down 4 units

But what is the correct order in performing these steps? I am not finding any succinct resources online that gives the rules for this.

Thanks!
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
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HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Confirming skeeter: If you were told that x= 2 how would you evaluate -f(x- 2)- 4? Before you could do anything else you would have to evaluate f(x- 2) when x= 2. An before you could do that you would have to calculate that if x- 2 then x- 2= 2- 2= 0.