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

the asymptote of g(x) is the aymptote of f(x) shifted six units up

Answer 2

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

$f(x)=7x$

$g(x)=7x+6$

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 $f(x)=mx+b$ is

$y=mx+b+\delta x$

Where, δx is infinitely small number, but not quite equal to 0.

The asymptote of f(x) is

$y=7x+\delta x$

The asymptote of g(x) is

$y=7x+6+\delta x$

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.