Question

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.

Answer 1

I believe the correct answer from the choices listed above is the last option. The statement about f(x) and g(x) that is true would be that the  asymptote of g(x) is the asymptote of f(x) shifted six units up. Hope this answers the question. Have a nice day.

Answer 2

The parent function is given by $f(x)= 7x$

and the transformation function is given by $g(x)= 7x + 6$

We can see that, 6 has been added to the function f(x) to get the function g(x).

We know that when we add some constant 'c' in the function then the function gets shifted upward by 'c' units.

Therefore, we will get g(x), when we will shift f(x) upward by 6 units.

Both functions are linear function hence, the asymptote of g(x) is the asymptote of f(x) shifted six units up.

D is the correct option.