$Parent function$: $f(x)$ = $\sqrt{x}$
$A$: the function is reflected in the y-axis and then translated 2 units to the right.
$B$: the function is translated 2 units to the right, then reflected in the y-axis.
for $A$, my working outs:
f(-x) - reflected in the y-axis
Now, I have a doubt. After reflected in the y-axis, will the transformation be included in the reflection?
i.e should it be: $f(-(x-2))$ or $f(-x+(-2))$
My understanding suggests that it should be $f(-x-2)$.
Similarly for $B$,
f(x-2) - two units to the right
Now, should it be
$f(-(x-2))$ or $f(-x-2)$
I think it should be $f(-x+2)$
I know, if it was reflected in the x-axis, and translated two units upwards, then it would have been:
$-f(x) + 2$
And, Reversing the operation: $-[f(x) + 2]$ = $-f(x) - 2$
That is why I have doubts regarding the order of reflection in the y-axis.
I would appreciate if you could provide an answer to my doubts.
The instruction for A clearly says "reflect, then translate". So you reflect first: $$f_1(x) = f(-x)$$ Then you translate the result: $$f_2(x) = f_1(x -2)$$ Similarly for B. Do the operations in the order that the problem says to do them.