Transformations

[TrueTears]

um just a small Q say you got a q saying "List the appropriate sequence of transformations that maps to "

so here obviously is the image and u re-arrange that to make it similar to , ie

then just equate and and etc etc

but say another q says "List the appropriate sequence of transformations that maps to " Do i do the same thing here? ie, 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?

[pHysiX]

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 units left
Dilate by a factor of  from the x-axis
Dilate by a factor of from y-axis

The dilation parts is equivalent to from the x-axis

[TrueTears]

yeah, thanks

but how would you do this algebraically?

[pHysiX]

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.

[kurrymuncher]

learning how to do it using mapping notation is pointless and wastes a lot of time too.

[pHysiX]

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. =]

[TrueTears]

thanks i get it now.