Final answer:
To find the graph of g(x) from f(x)=3x shifted six units to the right, replace x with (x-6) to get the equation g(x)=3(x-6), which simplifies to g(x)=3x-18.
Step-by-step explanation:
The graph of g(x) results from translating the graph of f(x)=3x six units to the right. When we translate a graph horizontally, we adjust the x variable within the function. To shift the graph of f(x) six units to the right, we substitute x with (x-6). Thus the equation of g(x) will be in the form g(x)=3(x-6).
To express this in a simplified form, we distribute the 3 inside the parenthesis: g(x)=3x-18. This new equation represents the original linear function f(x) shifted six units to the right on the x-axis.