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

Question

1 month ago

5

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.

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-02-25T04:34:10+03:00

Leona [12.6K]1 month ago

7 0

The asymptote of g(x) represents the asymptote of f(x) shifted six units upwards.

Inessa [12.5K] · Answer 2 · 2026-02-25T04:34:23+03:00

Answer:

The fourth option is correct: the asymptote of g(x) is the asymptote of f(x) shifted six units upwards.

Step-by-step explanation:

The functions provided are

$f(x)=7x$

$g(x)=7x+6$

Both functions are linear, and the domain of linear functions encompasses all real numbers.

Domain of f(x) = {x | x∈R }

Domain of g(x) = {x | x∈R }

Hence, options 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 an infinitesimal number, not equal to 0.

The asymptote for f(x) is

$y=7x+\delta x$

The asymptote for g(x) is

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

This indicates that the asymptote of f(x) is raised six units upward to obtain the asymptote of g(x).

Consequently, option 4 is correct: the asymptote of g(x) is the asymptote of f(x) shifted six units upward.

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

Further clarification

Learn more