Functions, is compression the inverse of stretch? In Function Transformation in the equation 
$Y= a[k(x-d)] + c$
We have a which is responsible for vertical stretch
.When it is $> 1$ we are told it's a stretch and then if it's $< 1$ we are told it's a compression but by the same factor.
Example
$Y=2x^2$.    Has a vertical stretch by factor of $2$
$Y=1/2x^2$.  Has a vertical compression by a factor of $1/2$
Isn't this wrong? Since compression is the inverse of stretch, shouldn't it be a compression by a factor of $2$? 
I say this since compression is the inverse of stretch, $1/2$ in compression is equal to $2/1$ stretch when inverses?
Am I correct, I am getting varying answers from different teachers and would like a definitive answer.
 A: I'm not sure you can get a definitive answer. Everyday English is often ambiguous or sloppy compared to formal mathematics.
I agree that a stretch by a factor of $1/2$ really compresses things, and one ought not say that it's a compression by a factor of $1/2$ (which is, for me, a stretch by a factor of $2$). 
The same problem occurs when someone says she incurred a loss of $-\$1000$. A negative loss is really a gain. but you do know what she meant.
A: These are just different conventions in the usage of English-language descriptions. There's no mathematical content to the disagreement. Each teacher is presumably following the language convention that they believe is the least likely to confuse you.
Personally, I tend to agree with your preferred convention. But I would also caution you not to be pedantic about it. If, out in the real world, someone says "our budget shrank by a factor of a half" and you smugly object "oh, so your budget doubled?" then you're just being obtuse.
A: Hmm okay i understand that it's a word that makes the difference, but I guess I'll have to stick with my teacher's way because if not I'll get marks off!
