Answer:
The correct option is 4. The asymptote of g(x) is the asymptote of f(x) shifted six units up.
Step-by-step explanation:
The given functions are


Both are linear function and the domain of a linear function is all real real numbers.
Domain of f(x) = {x | x∈R }
Domain of g(x) = {x | x∈R }
Therefore option 1 and 2 are incorrect.
The linear asymptote of a linear function
is

Where, δx is infinitely small number, but not quite equal to 0.
The asymptote of f(x) is

The asymptote of g(x) is

It means the asymptote of f(x) shifts six units up to get the asymptote of g(x).
Therefore option 4 is correct. The asymptote of g(x) is the asymptote of f(x) shifted six units up.