Transformations

[kefoo]

hey guys, just wondering if anyone has a fully detailed explanation of each of the transformations?
sometimes my teacher says 'In y-axis' and 'Around y-axis' and 'from y-axis'
I'm just confused about each of them, so if anyone can give me some examples of each, that'd be really cool

[iNerd]

Same!

Esp 'parallel' and 'from'

[Bonifacio]

Well firstly, when dealing with dilations, think of 'from the x-axis' as things literally moving away from the line y=0.
Similarly, when thinking of 'from the y-axis' think as things literally moving from the line x=0.

Once you have that mindset, much of it becomes a lot easier.

Furthermore, read chapter 3 from the year 12 Essential methods textbook for an in depth discussion on these terms.

[kefoo]

Thanks for that Bonifacio, but there's also this that confuses me. One is;
Q: Transform x^2 to -(2x - 6)^2 + 4
-Reflection in y-axis
-Dilation of 1/2 from y-axis <- don't understand why it's 1/2?
..

[Greatness]

you have to take out the 2 as a common factor i.e. make x a single term, if that makes sense.
so that eqn will become: y=-2(x-3)^2 + 4
thus a=2 so dilation by a factor of 1/2 from y axis

[Bonifacio]

Ok so the basic form is y=x^2

Your changed equation is y = -(2x-6)^2 +4

Change it to look like this:

y-4 = -(2x-6)^2


4-y = (2x-6)^2

4-y = y'

-y= y'-4

y=-y'+4

2x-6 = x'

2x = x' +6

x = x'/2 + 3

Therefore:

Reflection in the x-axis, Dilation of factor 1/2 from the y-axis, translation of 3 units in positive direction of x-axis and 4 units in positive direction of the y-axis.

These problems become immensely difficult if you don't use mapping as I have used.

[Bonifacio]

you have to take out the 2 as a common factor i.e. make x a single term, if that makes sense.
so that eqn will become: y=-2(x-3)^2 + 4
thus a=2 so dilation by a factor of 1/2 from y axis

Hmmm, are you aware that 2 (x-3)^2 does not equal (2x - 6)^2?

[kefoo]

Find the rule of the image when y = 1/(x^2) + 2 is translated 5 units in the negative direction of the x-axis and 1 unit in the positive direction of the y-axis then dilated by a factor of 2 from the y-axis. (From Practise SACS/Tests sticky thread)

would it be 2/(x^2 + 5) + 3? seeing if i'm doing this right

[luken93]

Into eq:

[dooodyo]

Hey Kefoo do you go to Parade College by any chance?

[jinny1]

Lets say: y=-4(x-3)^2 + 4


then how would you know which transformations occured to it from y=x^2

because you could have a different translations but it wud still end up the same equations with different dilation factors...

[Water]

 y=-4(x-3)^2 + 4


You'd look at x


x` - 3 = x

x` = x + 3

So there has been a translation of 3 units to the right in the x axis.



And you look at y`


(y`-4)/-4 = y

y` =  -4y + 4


There was a dilation factor of 4 from the y axis

There was a reflection in the x axis

There was a translation of 4 units in the positive direction of the y axis..

[jinny1]

y=-4(x-3)^2 + 4


And you look at y`


(y`-4)/-4 = y

y` =  -4y + 4

Thanks!

but i dont get how you got the y part.

And you look at y`


(y`-4)/-4 = y

y` =  -4y + 4

[Water]

y` =-4(x-3)^2 + 4

       


Ignore the x transformation, so it'd be


y` = -4(x)^2 + 4



y`-4 = -4x^2


(y`-4)/ -4 = x^2



(y`-4)/ -4 = Transformation of y.