I think it is the notation of this function transformation problem that I am messing up

[mickey222]

I assume it is the notation that has me repeatedly failing the answer to this problem. Here is the problem:

1. The function g(x) is the transformation resulting from vertically stretching f(x) by a factor of 8, horizontal shift 6 units to the left and 7 units down.
Instructions: Express the function g(x) in terms of the function f(x).

g(x)= ?


I thought this one would be pretty easy, but I can't seem to come up with the answer. I thought the answer was f(8x+6)-7, but alas this is not it. There must be something I am not comprehending.

 

[mickey222]

8f(x+6)-7

ah I got it, but to be honest I am not quite sure of the difference in my answers, or rather, what the differences express. I figured that in my previous answer, what I was actually doing was rewriting what f(x) was, instead of expression a transformation of the original f(x). I am guessing that putting the 8 in front of the F achieves the latter instead of the former.

 

[lev888]

I assume it is the notation that has me repeatedly failing the answer to this problem. Here is the problem:

1. The function g(x) is the transformation resulting from vertically stretching f(x) by a factor of 8, horizontal shift 6 units to the left and 7 units down.
Instructions: Express the function g(x) in terms of the function f(x).

g(x)= ?


I thought this one would be pretty easy, but I can't seem to come up with the answer. I thought the answer was f(8x+6)-7, but alas this is not it. There must be something I am not comprehending.

Function Transformations

www.mathsisfun.com

 

[Steven G]

Forget the -7 for now as it is in examples.
When we plug in a real number, say 3, for x in f(x+6), we get back a real number, say 11. So f(3+6) = 11. Now 8f(x+6) is simply 8 times f(x+6). So 8f(3+6) = 8*11 or 88. The 8 in front just multiplies f(x+6) by 8.

Now if x is multiplied by 8, that is very different. Now we have f(8x+6). If x=3, then we have f(8*3+6) = f(30) which has nothing to do with 8f(3+6).

If this is still unclear then try what I did above for a specific function.

 

[mickey222]

Both answers make sense, thank you. In my lesson, I was taught nothing about the difference between vertical and horizontal stretching, so that's where the lapse in understanding was.