Transformations of functions

[Nephix]

Hey whats going on guys, would it be possible for someone to help me out with some work relating to transformations?

The graph of Y = 2/(3x+1)^2 +4 (Truncus) has been dilated parallel to the y-axis by a factor of:

My first thought for some reason is 2, but because there is a coefficient of X are we supposed to get X by itself to find the dilation?

Any help would be great, thanks

[abcdqd]

Hey whats going on guys, would it be possible for someone to help me out with some work relating to transformations?

The graph of Y = 2/(3x+1)^2 +4 (Truncus) has been dilated parallel to the y-axis by a factor of:

My first thought for some reason is 2, but because there is a coefficient of X are we supposed to get X by itself to find the dilation?

Any help would be great, thanks

you are right

[Nephix]

ok sweet as, thanks

[FlorianK]

nah, it's dilated by (1/2) in the y-direction and (1/3 ) in the x-direction.
MUST READ THE QUESTION!!!!!

[b^3]

nah, it's dilated by (1/2) in the y-direction and (1/3 ) in the x-direction.

He was right the first time since we are looking for the transformations that would take the standard truncus curve to that of the one given.



Compare to

Parallel to the axis is the same as 'from' the axis.



That is we have a translation of unit in the negative direction of the axis and units in the positive direction of the axis, then a dilation by factor from the axis and a dilation of factor from the axis.

You can look at it graphically to check as well. Try moving the and sliders.
https://www.desmos.com/calculator/zhxwo5yb9g

[Planck's constant]

I think I'll go with a dilation factor of 2/9 parallel to the y axis.

I choose 2/9 because there are theoretically infinite combinations of dilations from the x- and y- axis which produce the given image, therefore I interpret the problem as requiring a single dilation from the x-axis and nothing else (other than translations)

Hence, 2/9