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# Transformations of trig graphs :\ watch

1. I'm confused here.

So if you have f(x)
f(x-a) shifts f(x) across to the right a units, right?
and f(-a) relfects in y axis, right?

then you do y=sin(-x)
then you want to shift this say, pi/2 to the RIGHT say, surely this would be sin(-x-pi/2)

but it isn't, that shifts it to the left. What's going on?
2. I'm confused here.

So if you have f(x)
f(x-a) shifts f(x) across to the right a units, right?
and f(-a) relfects in y axis, right?

then you do y=sin(-x)
then you want to shift this say, pi/2 to the RIGHT say, surely this would be sin(-x-pi/2)

but it isn't, that shifts it to the left. What's going on?
Use the symmetry properties of sin and cos to work this out, i.e.

So with your example, you have

y = sin(-x) = -sin(x)

so to shift this to the right, try

y = -sin(x-pi/2)
3. (Original post by ziroic)
then you do y=sin(-x)
then you want to shift this say, pi/2 to the RIGHT say, surely this would be sin(-x-pi/2)
You've added pi/2 to x there: the transformation taking sin(-x) --> sin(-(x + pi/2)) is a shift to the left by pi/2.
4. The addition or subtraction of a constant to move the graph of a function left or right is applied to the variable "x".

So, as I'm sure you are aware, to move x^2 to the left by 1, you change the x^2 to (x+1)^2.

The change is applied to the x, before you apply any other operation to the x.

In like fashion, if your function was simply -x; to move it to the left by 1, you add 1 to the x, not to the -x.
So you would end up with -(x+1), which becomes -x-1 when you expand the brackets.

The minus in front of the x, is an operation on the x, and you need to make your change before that operation is applied, hence the -(x+1).

Hope that helped.
5. (Original post by ziroic)
I'm confused here.

So if you have f(x)
f(x-a) shifts f(x) across to the right a units, right?
and f(-a) relfects in y axis, right?

then you do y=sin(-x)
then you want to shift this say, pi/2 to the RIGHT say, surely this would be sin(-x-pi/2)

but it isn't, that shifts it to the left. What's going on?
so much worries at 11.35

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