Potentially overthinking transformations of functions... need confirmation So this may be really simple. The question is

Write the equation of the transformed function $y=x^2$ after the following transformation in the order given.

*

*a vertical compression by a factor of $\frac13$ followed by a transformation of $3$ units right.


Isn't this just $y=3\left((x-3)^2\right)$?
I feel as though I'm overthinking it.

For any function $y=f(x)$, transformations can be described by the equation
$$y=af[k(x-c)]+d$$
where $|a|$ is the vertical dilation, $|k|$ is the horizontal dilation, $c$ is the horizontal translation, and $d$ is the vertical translation.  If $a<0$, there is a vertical reflection, and if $k<0$, there is a horizontal reflection.
Thus, a vertical compression by a factor of $3$ would mean $a=\frac13$, and a horizontal translation $3$ units right would mean $c=3$.  Therefore, we have
\begin{align}
f(x)&=x^2\\
y=\frac13f(x-3)&=\frac13(x-3)^2
\end{align}
You've got the right answer!
