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transforming graphs

1) give a simple set of transformations which when applied in sucession take y=x^2 to y=4-2x+x^2

i dunno how to do this because i dont understand where the -2x comes from!

2)write down two simple transformations that will transform
y=cos x
to
y=sin(3x+1/2 pi)
does the order of transformations matter?

for this one i thought it would be a stretch in x direction factor 1/3 then translate 1/2 pi in neg x direction but the answer says the other way round could someone explain?

thanks alot

Reply 1

Gaz031

sarah12345

1) give a simple set of transformations which when applied in sucession take y=x^2 to y=4-2x+x^2

i dunno how to do this because i dont understand where the -2x comes from!

y=f(x-1) + 3.

2)write down two simple transformations that will transform
y=cos x
to
y=sin(3x+1/2 pi)
does the order of transformations matter?
Try using the fact that cosx = sin[0.5pi-x].
I don't think order of transformations matters.