Which statement about f(x) and its translation, g(x), is true? f of x is equal to 7 to the x th power g of x is equal to 7 to the x th power plus 6
Answer
A
The domain of g of x is start set x such that x is greater than 6 end set , and the domain of f of x is start set x such that x is greater than 0 end set .
B
The domain of g of x is start set y such that y is greater than 0 end set , and the domain of f of x is start set y such that y is greater than 6 end set .
C
The asymptote of g of x is the asymptote of f of x shifted six units up.
D
The asymptote of g of x is the asymptote of f of x shifted six units down.
Explanation
Since g(x) = 7^x + 6, it is the graph of f(x) = 7^x shifted 6 units up. The horizontal asymptote of f is y = 0, so the asymptote of g is y = 6. Therefore, g’s asymptote is f’s asymptote shifted six units up.
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