Sketch graph as function of another

[geft]

Sketch g(t) = f(-3t + 9).

I know how to work this out with trial and error:

t = 0 => g(t) = f(9) = 0
t = 1 => g(t) = f(6) = 0
t = 2 => g(t) = f(3) = 2
t = 3 => g(t) = f(0) = -3
t = 4 => g(t) = f(-3) = 0
etc...

How do I do this in a faster and more reliable way, taking into account all the coordinates?

 

[geft]

I asked around and it turns out I needed to do this visually.

f(-3t + 9) = f(-3[t-3])

1. Compress f(x) -> f(3x)
2. Time reverse f(3x) -> f(-3x)
3. Time shift f(-3x) -> f(-3x[t-3])

 

[HallsofIvy]

Since you never told us what "f" was, it was impossible to make sense out of your question or your graph.