Understanding the Graphing Transformation $a-x$

Question

I was attempting to graph the function $y(x)=\frac{\ln x}{x}$ and apply numerous transformations to it. One of them was graphing $y(a-x)$. The way that I tried to tackle it was as follows:

1. Graphed $y(-x)$, which is just a reflection of the graph about the y-axis.
2. Graphed $y(-x + a)$, which I thought should be the graph in step 1, slides to the left by $a$ units, as the graph $y(x-a)$ slides the graph to the right $a$ units.

However, this was not the case, it seemed when I used graphing software that it shifted it the graph in step 1 to the right $a$ units.

Question: What was wrong in my thought processes? Could someone perhaps explain a better method of obtaining the graph?

Thanks