Transformations help please!

[homosapiens]

Would appreciate some clarification:

1. f(x) is sin(x). What would the transformed equation be after:
a) a dilation in the x direction by 3, then horizontal translation to the right by 2
Is sin(1/3*(x-2)) correct?
b) horizontal translation to the right by 2, then a dilation in the x direction by 3
Is the answer the same as a?

c) a reflection in the y-axis followed by horizontal translation to the right by 2
f(-x-2) or f(-(x-2)
d) horizontal translation to the right by 2, followed by a reflection in the y-axis
f(-(x-2)) ?

e) vertical translation by 2 up followed by reflection in the x-axis
-(f(x)+2) ?
f) reflection in the x-axis followed by vertical translation of 2 units up
-f(x)+2 ?

[dc302]

1
b) no they're not the same, it would be sin(x/3  - 2)

c) the second one is right.
d) no it would be f(-x - 2)

e, f are correct

[homosapiens]

Thanks heaps!