Say that I have a function $f(x)$ with range $(-\infty,10]$ and a function $g(x)$ where $g(x)=2f(-x)-3$, what is the range of $g(x)$?
So do I do the vertical shift first or do I do the vertically stretching first? I can't just stretch it first and then shift down 3 and have the new range be $(-\infty,17]$? Does the stretching factor matter? Or should it just be $(-\infty,7]$?