Combined input transformations

For y=f(ax+b), a 0, track the original input u by ax+b=u. A point (u,v) moves to (u-ba,v). Equivalently, first scale horizontally by 1|a|, reflect in the y-axis if a<0, then translate horizontally by - ba. Example For y=f(2x-6), compress horizontally by scale factor 12, then move right by 3. The point (4,7) moves to (5,7). For y=Af(ax+b)+B, the full point mapping is (u-ba,Av+B). Apply the same mapping to domain endpoints and relevant asymptotes.