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kotegsom [21]
3 years 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:
Cloud [144]3 years ago
7 0
The asymptote of g(x) is the aymptote of f(x) shifted six units up
Oksanka [162]3 years ago
5 0

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.

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