ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: TrueTears on February 28, 2009, 11:32:01 pm

Title: Transformations
Post by: TrueTears on February 28, 2009, 11:32:01 pm: um just a small Q say you got a q saying "List the appropriate sequence of transformations that maps $y = \sqrt{x}$ to $y = 2\sqrt{3x+5}-7$ "

so here obviously $y' = 2\sqrt{3x'+5}-7$ is the image and u re-arrange that to make it similar to $y = \sqrt{x}$ , ie $\frac{1}{2}(y'+7) = \sqrt{3x'+5}$

then just equate $y = \frac{1}{2}(y'+7)$ and $x = \sqrt{3x'+5}$ and etc etc

but say another q says "List the appropriate sequence of transformations that maps $y = \frac{6}{(1-2x)^2} - 1$ to $y = \frac{1}{x^2}$ " Do i do the same thing here? ie, $y' = \frac{1}{x'^2}$ is now the image ? But how do u re-arrange the image to fit the given equation? Or do you re-arrange the given equation to fit the image?
Title: Re: Transformations
Post by: pHysiX on March 01, 2009, 02:59:29 pm: wat my teacher taught me is to "undo" the things. I always followed a certain sequence for transformations. so in this case, just do the opposite; reverse the translations, then undo the reflections then undo the dilations. so i think it's:

Shift of 1unit up
Shift of $\frac{1}{2}$ units left
Dilate by a factor of $\frac{1}{3}$ from the x-axis
Dilate by a factor of $2$ from y-axis

The dilation parts is equivalent to $\frac{2}{3}$ from the x-axis
Title: Re: Transformations
Post by: TrueTears on March 01, 2009, 03:01:53 pm: yeah, thanks

but how would you do this algebraically?
Title: Re: Transformations
Post by: pHysiX on March 01, 2009, 03:04:39 pm: hmmm did i get it right? algebraically eh?...give me a bit coz i don't like using mapping notation. can never seem to make it work.

haha i think i've got it:

let y=6...be the original. y=1/x^2 be the image --> y'=1/(x')^2

so y=(3/2)/(x-.5)^2 -1

(2/3)(y+1)=y'

so it's clear that there is:
a translation of 1 up, dilation of 2/3 from the x

the x part is similar. hope it makes sense.
Title: Re: Transformations
Post by: kurrymuncher on March 01, 2009, 03:59:20 pm: learning how to do it using mapping notation is pointless and wastes a lot of time too.
Title: Re: Transformations
Post by: pHysiX on March 01, 2009, 04:27:49 pm: well learning mapping notation is not all pointless because it develops the understanding necessary for using a "shortcut". but yes, it's a big waste of time. =]
Title: Re: Transformations
Post by: TrueTears on March 01, 2009, 04:48:11 pm: thanks i get it now.