Graphing Transformations :(

I'm going insane. I can't figure out how the book is getting one answer and me a completely different.

So here's the problem:

Graph using transformations: f(x)=1/4x^2-2

My process:

y = x^2

x|y

-2|4

-1|1

0 |0

1 |1

2 |2

so next would be this right?

y=1/4(x^2) so y * 1/4, right? according to the book, WRONG!

The book says that the next step would be a vertical compression of 2. What? huh? Where the hell is there a *2 in this?

I'm sure it's some algebra that I'm just over looking, but any help at all would be appreciated!

Re: Graphing Transformations :(

1 Attachment(s)

Re: Graphing Transformations :(

Hi emakarov,

Appreciate the reply! That kinda makes sense, except it's seriously not what it says in the book. I'm starting to think it's just wrong and trying to screw me up. Decided to take a picture of the book, as I'm still confused :\

#21

Also, doesn't it just contradict #19 ...

Attachment 23429

Re: Graphing Transformations :(

Yes, it must be a mistake in the textbook because of the difference between #19 and #21.

I personally think that *compressing* vertically by a factor of means changing every point into . In contrast, *stretching* vertically by a factor of means changing every point into . Thus, compressing by a factor of is stretching by a factor of , so it is sufficient to always use the term "stretching." With this convention, both #19 and #21 involve stretching of y = x^2 by a factor of 1/4, or compressing it by a factor of 4. One does not have to follow this convention; for example, one may always use both "stretching by " and "compressing by " for the transformation , but use the word "stretching" for factors > 1 and "compressing" for factors < 1. However, above all, terminology has to be consistent, which it is not in the textbook.

Edit: LaTeX.

Edit2: Clarified the alternative convention.