Answer:
d. The asymptote of g(x) is the asymptote of f(x) shifted six units up.
Step-by-step explanation:
The complete question is
f(x) = 7x g(x) = 7x + 6 Which statement about f(x) and its translation, g(x), is true?
a. The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}.
b. The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}.
c. The asymptote of g(x) is the asymptote of f(x) shifted six units down.
d. The asymptote of g(x) is the asymptote of f(x) shifted six units up.
The initial function is
[tex]f(x)=7x[/tex]
After the translation, the function is
[tex]g(x)=7x+6[/tex]
If you compare, you'll notice that the transformation was about adding 6 units to g(x). This means that the function is being translated upwards 6 units, because such change is to g(x) which represents the vertical axis.
Additionally, after this transformation neither the domain or range change, because the range and domain of a linear function is always all real numbers.
Therefore, the right answer is D, because describes the transformation.
