Move, stretch and flip a graph

Every change to a graph moves each point in a simple way. You will write the moves for a shift, a stretch and the two flips, and follow one point through them.

The idea. On $y = f(x - h) + k$ the point $(p, q)$ goes to $(p + h, q + k)$. On $y = a\,f(x)$ it goes to $(p, aq)$. On $y = f(-x)$ it goes to $(-p, q)$.

Your tasks.

1. In shift, return the image of pt on $y = f(x - h) + k$.
2. In stretch, return the image of pt on $y = a\,f(x)$.
3. Fill trail with the images of $(3, 4)$ on $y = f(x - 2) + 1$, $y = -f(x)$ and $y = f(-x)$.