1. ## 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!

2. ## Re: Graphing Transformations :(

You are right that the next step is vertical compression by 4 (i.e., multiplying y by 1/4).

Originally Posted by epiclairs
The book says that the next step would be a vertical compression of 2.
Maybe it's horizontal expansion by 2? If $\displaystyle f(x) = x^2$, then $\displaystyle x^2/4=f(x/2)$, i.e., the graph of $\displaystyle x^2/4$ is obtained from the graph of f(x) by changing each (x, y) into (2x, y).

In other words, compressing the parabola $\displaystyle y=x^2$ vertically by 4 and expanding it horizontally by 2 give the same result.

3. ## 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 ...

4. ## 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 $\displaystyle \alpha$ means changing every point $\displaystyle (x, y)$ into $\displaystyle (x, y/\alpha)$. In contrast, stretching vertically by a factor of $\displaystyle \alpha$ means changing every point $\displaystyle (x, y)$ into $\displaystyle (x, \alpha y)$. Thus, compressing by a factor of $\displaystyle \alpha$ is stretching by a factor of $\displaystyle 1/\alpha$, 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 $\displaystyle \alpha$" and "compressing by $\displaystyle \alpha$" for the transformation $\displaystyle (x,y)\mapsto (x,\alpha y)$, 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.