I have a conceptual problem.
If the graph of a function $f(x)$ has to be horizontally shifted to the right by $a$ units, then the new graph is $f(x-a)$.
However, if the graph has to be reflected about a vertical line, e.g. $x=3$, then the graph needs to be translated by $3$ units to the left, reflected and shifted back to the right by $3$ units (as described here). According to the rule above, the new graph should be $$f(x) \rightarrow f(x+3) \rightarrow f(-x-3) \rightarrow f(-x-3-3)=f(-x-6)$$ This is wrong, and the right answer $f(6-x$) can only be achieved by switching the operations $±3$ for translating to the left and to the right.
Could someone enlighten me?