Function graph transformations I'm looking for a reliable document with formal mathematical justification of how and why graph transformations work. Given a function $f(x)$, what is the graph of $f(a-x)$? Why should we shift $f(x)$ by $a$ to the right in this case?
Imagine someone read a paper about graph transformations, like this one.
Intuitively, someone could say: well, $f(a-x)$ is a graph of $f(-x)$ shifted left by $a$ because we are adding $a$, right?
Is there a more elegant and formal way to prove what those transformations to graphs result in?

The graph of $x\mapsto f(x+a)$ is just the composition of $f$ with the translation $x\mapsto x+a$. Therefore, if $D$ is the domain of $f$, the graph of $x\mapsto f(x+a)$ is the same graph than $f$ but on the domain $D+a$.
