Function Notation Transformation

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

If g(x) = 6(-8x + 12) + 7, what is the value of g(6)?

Given $$g(x)=f(x-3)+5$$ . What transformations took place from the original function f(x)? The graph shifted (a)   3 units and ​ (b)   5 units.

If g(x) = 2(-5x +2) + 10, what is the value of g(4)?

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?