Confused about transformation questions

Well if I stretch by s.f. 2 in the y direction and s.f. 1/2 in the x-dir I'd get

\frac{y}{2}=(2x)^2+2

Reply 3

So for Describe a single transformation that would map the graph of y = x^2 + 2 onto the graph of y = x^2+4x+6

I put translated by vector [-4,6] but the answer says translation by 2 units in -ve x direction. Is it because it's x^2, so you put -2 in instead of -4? Mad confused lol

Reply 4

x^2+4x+6=(x+2)^2+2

which is a translation by -2 along the x-axis from

x^2+2

Reply 5

Original post by the bear

so if f(x) is x² + 2 then 2f(x) is 2( x² + 2 )

So when you stretch in the y direction you times everything by the sf?

Reply 6

The simple rule is that when you stretch in the y-dir by s.f.

a

, you simply take

y

and replace it by

\frac{y}{a}

. Similarly if its along the x-axis. Just take

x

and replace it by

\frac{x}{a}

.

If it's a translation along the y-axis by

b

, then you take

y

and replace it by

y-b

. Similarly for the x-axis.

Then all you need to do is just rearrange to get

y=...

or whatever form they ask for.

EXAMPLE:

y=x^2-4x+10

can be rewritten as

y=(x-2)^2+6

which in turn gives

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

which is clearly a translation by vector

[2,4]

from the graph

y=x^2+2

as you simply replace

x \mapsto (x-2)

and

y \mapsto (y-4)

(edited 6 years ago)

Reply 7

[QUOTE="RDKGames;74371654"]The simple rule is that when you stretch in the y-dir by s.f.

a

, you simply take

y

and replace it by

\frac{y}{a}

. Similarly if its along the x-axis. Just take

x

and replace it by

\frac{x}{a}

.

Ok, so if I was to enlarge y=x^2 + 2 by sf 2 in Y direction I would do y/2=x^2+2 which makes y= 2x^2 + 4?

And If I was to do enlarge by sf 2 in x direction I'd do y = (x/2)^2 + 2, which makes y = x^2 /4 +2?

Original post by RDKGames

EXAMPLE:

y=x^2-4x+10

can be rewritten as

y=(x-2)^2+6

which in turn gives

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

which is clearly a translation by vector

[2,4]

from the graph

y=x^2+2

as you simply replace

x \mapsto (x-2)

and

y \mapsto (y-4)

Ah ok. So since its x^2 + 2 -> x^2+4x+6 I would do

y = (x+2)^2 +2, so its a translation by [-2,0]?

Is that the main way to do it? Because for a harder question I would be a lot more difficult to see what to put into the bracket

Reply 8

That's the main way to do it, and you can clearly see these match the answers in your book - they're all correct. If you find one you cannot do using these principles, post it here and we'll give you a hint.

Reply 9

Original post by RDKGames

Ok thanks man :smile:

A level maths is legit killing me

Reply 10

Original post by RDKGames

If i was to enlarge (x+9)^3 + 2(x+9)^2 + 10 by a scale factor of 2 in the y direction would I do y/2 = (x+9)^3 + 2(x+9)^2 + 10, which gives me

2(x+9)^3 + 4(x+9)^2 + 20? I put it in desmos but it doesn't look right

Reply 11

Why doesn't it look right?

It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the

y<0

region gets stretched twice downwards. Everything is as expected.

Mad ting

Original post by RDKGames

Why doesn't it look right?

It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the

y<0

region gets stretched twice downwards. Everything is as expected.

sh*tden

thanks

Reply 14

Original post by RedGiant

Mad ting

yo i'm baffed with life. i'm not bad at maths you know but this graph stuff is confusing the hell out of me

Reply 15

RedGiant

I can see m8, what exam board are you with?

And thx for follow ^^

Reply 16

Original post by RDKGames

Why doesn't it look right?

It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the

y<0

region gets stretched twice downwards. Everything is as expected.

When reflecting in the y axis, do you times all the x by -1, and when reflecting in the x axis, do you times everything by -1?

Original post by RedGiant

I can see m8, what exam board are you with?

And thx for follow ^^

edexcel, u?

following so i can dm for maths and chat u up

Reply 17

RedGiant

I'm on edexcel as well (done chapters 1-7 but don't know which bit of the spec this is)

Reply 18

Same principles as above. Reflection in the y-axis means

x \mapsto (-x)

and reflection in the x-axis means

y \mapsto (-y)

.

Wasn't this covered in GCSE reflections of graphs or something...?

Reply 19