Basic relationships between functions

Question

I am working through the Mooculus course. Can someone explain what is going on here?

The question:

If f(2)=2 and g(x)=4⋅f(x), what point can you determine on the graph of g?

This comes in the hint:

You only have information about a point where x=2.

At this point we have g(2)=4⋅f(2).

Substituting f(2)=2 we have g(2)=4⋅2.

So g(2)=8.

Thus (2,8) is on the graph of g.

Thanks

Answer 1

For the $(1,-3)$ example:

You only know about the point $x=5$ so put $x=5$ into $f(x)=g(x−4)$.

Then $f(5)=g(5−4)=g(1)$.

So $g(1)=f(5)=-3$ and this gives you the point $(1,-3)$.