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Transformation expression

Hi,

Looking for some help on how to find an expression for a function after a transformation.
Ok, so basically I was asked to sketch the graph of f(x) = 1/x , which was easy enough, then to sketch the transformation of (2, 3). Afterwards I was asked to find an expression for g(x), which is the f(x) after the transformation. Not too worried about the answer itself, more looking into the actual method for future questions.

Thanks a lot!
Reply 1
By transformation do you mean a translation of vector (2,3)?
Reply 2
Original post by Jordan97
By transformation do you mean a translation of vector (2,3)?


yeah sorry if I didn't use the right terminology :P
Original post by jack.hutch
yeah sorry if I didn't use the right terminology :P


f(x-a) moves a to the right

f(x) + b moves b up
Reply 4
Original post by TenOfThem
f(x-a) moves a to the right

f(x) + b moves b up


yeah I know but I'm not sure how I would right the transformed function into an equation
Original post by jack.hutch
yeah I know but I'm not sure how I would right the transformed function into an equation


I am not sure what you mean - you would put g(x) = and then apply the -a and +b that I showed
Reply 6
Sorry maybe I'm not making myself clear, maths is not my strong point, haha.

Here is a photo of the question:

IMG_6267.jpgIMG_6267.jpg
Reply 7
the vertical asymptote, previously at x=0 will now be at x=2

the horizontal asymtote, previously at y=0 will now be at y=3.

g(x)=1xa+b\displaystyle g(x)= \frac{1}{x-a}+b

(transformation vector (a,b)

as x-> +/- infinity, y->b
as x->a from left/right, y->??

when y=0, x=?

when x=0, y=?
(edited 9 years ago)
Reply 8
Original post by jack.hutch
Sorry maybe I'm not making myself clear, maths is not my strong point, haha.

Here is a photo of the question:

IMG_6267.jpgIMG_6267.jpg


pretty much covered by the guys above, the (2,3) indicates which (x,y) directions you shift the graph you have.
Reply 9
alright thanks a lot guys!
Reply 10
Original post by Hasufel
the vertical asymptote, previously at x=0 will now be at x=2

the horizontal asymtote, previously at y=0 will now be at y=3.

g(x)=1xa+b\displaystyle g(x)= \frac{1}{x-a}+b

(transformation vector (a,b)

as x-> +/- infinity, y->b
as x->a from left/right, y->??

when y=0, x=?

when x=0, y=?


actually sorry, but why would it be -a and not +a?
Original post by jack.hutch
actually sorry, but why would it be -a and not +a?


in the translation vector, the (2,3) which really means (+2,+3) indicates the increase in the positive direction of each co-ordinate, but when we come to represent that in graphs, for the y, this is the usual way: y=f(x) +3 means up in the positive y direction, y= f(x) - 3 means 3 units down.

The x direction is exactly the opposite: y= f(x-2) means 2 units up the positive x axis.

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