F(x) = 7x g(x) = 7x + 6 which statement about f(x) and its translation, g(x), is true? the domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}. the domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}. the asymptote of g(x) is the asymptote of f(x) shifted six units down. the asymptote of g(x) is the asymptote of f(x) shifted six units up.

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.