Transformations HELP!

[DavidSheena]

I came across question where you had to apply a series of transformations to a equation. It read as follows:

The graph of the function with the rule y= x^(2/3) is transformed with the following:
-A dilation by a factor of 2 from the y-axis.
-A reflection in the x-axis
-A translation of +4 units parallel to the x-axis
-A translation of +1 units parallel to the y-axis.

My working was:

y=f(x) becomes, y=f(x/2), becomes, y= -f(x/2), becomes y= -f(x/2-4)+1

So my solution was y= -(x/2 -4)^(2/3) +1

But the answer is y= -((x-4)/2)^(2/3) +1

I thought mine would be correct since the translation was applied after the dilation and not before? Would appreciate if anyone could explain?

[dc302]

You're very nearly right. The problem is when you applied the translation 4units in the x direction. When you do this, u have to change x to x-4.

So from y=-f(x/2), it becomes y = -f((x-4)/2)

[DavidSheena]

Oh, thank you! Just to clarify it's because your applying the translation to x, not to the whole thing inside the brackets?

[dc302]

You could think of it that way, yes.