Maths Methods 3/4 Help Thread 2011

[Niskii]

Probably a really simple question about transformations, but:

If you have , and the question says translate it one unit right, giving , what happens if if it then asks you to dilate it by a factor of 1/2 from the y-axis?

Would it be or which is the same as ?

My teacher said that if you let what's inside the brackets equal 0, the result should always be what it was translated by (e.g. in this case for the you'd have 2x-1=0, x=1/2 which is wrong because it was meant to be translated 1 right instead of 1/2), but this doesn't seem to match up with the answers to some of the practice questions I've done.

Thanks!

[xZero]

from my understanding (2x-1)^2 should be correct, if you translate a graph before the dilation, the translation will be dilated according to the dilation factor. (hope it makes sense xD)

[enpassant]

it would be (2x-1)^2

[pi]

it would be (2x-1)^2

Could you please explain? I'm pretty bad at transformations... Would like to know to.

[Greatness]

which is the same as ?

They dont equal each other if you expand do they? This where i have gotten confused in the past :s

[xZero]

it would be (2x-1)^2

Could you please explain? I'm pretty bad at transformations... Would like to know to.

If you translate the graph before the dilation, the translation will be dilated. So if you translated the graph 1 unit to the right, the x-intercept will be at x=1. Then if you dilate the graph by 1/2 from the y-axis, it pulls the graph towards the y-axis, including the x-intercept and the new x-int will be at 1/2

[pi]

oh, thanks xZero

[Niskii]

Thanks heaps to everyone that replied

Haha, don't worry, that makes perfect sense xZero!

I think I get it now, I suppose my teacher must have forgotten to add in that a dilation after the transformation affects the transformation.

@swarley: I think they do equal each other, because it's just expanding within the squared? Like normally if you had 2(x-1) you would expand to 2x-2 (both forms are equivalent), except in this case it's just inside the . I think so anyway

[xZero]

the expansion's correct but I don't understand where (2(x-2))^2 came from oO

[Niskii]

Oh, that's from my original question, because I wasn't sure if the 2 from the dilation by 1/2 multiplies just the x term or the whole bracket (thus 2(x-1)).

I do get now that the answer is (2x-1)^2, though!

[luken93]

So does it then matter if you had say:
Dilate by 1/2 y axis
Then translate right by 1?

[xZero]

Yes, the ordering of these transformations is really important since we can express all the transformation in matrices and we know that the ordering of multiplication in matrices can change the outcome by miles.

If you dilated by 1/2 you will get y=(2x)^2 then translate and you will get y=(2(x-1))^2

[luken93]

Yes, the ordering of these transformations is really important since we can express all the transformation in matrices and we know that the ordering of multiplication in matrices can change the outcome by miles.

If you dilated by 1/2 you will get y=(2x)^2 then translate and you will get y=(2(x-1))^2

Yep, that's what I thought.

So as long as you think about it logically (x ints and dilating them), then it's really the only way to do it?

[kefoo]

1. For pi/2 < x < pi with cos x = -sin(pi/6) find x
2. For pi/2 < a < pi with cos a = -sin(b) where 0 < b < pi/2

i just dont understand these questions

[xZero]

Yes, the ordering of these transformations is really important since we can express all the transformation in matrices and we know that the ordering of multiplication in matrices can change the outcome by miles.

If you dilated by 1/2 you will get y=(2x)^2 then translate and you will get y=(2(x-1))^2

Yep, that's what I thought.

So as long as you think about it logically (x ints and dilating them), then it's really the only way to do it?

yeh i suppose so

1. For pi/2 < x < pi with cos x = -sin(pi/6) find x
2. For pi/2 < a < pi with cos a = -sin(b) where 0 < b < pi/2

i just dont understand these questions

1)



i don't quite understand the second question o_o