Which statement about f of x and its translation, g of 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 asymptote of g of x is the asymptote of f of x shifted six units down.
B
The asymptote of g of x is the asymptote of f of x shifted six units up.
C
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 .
D
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 .
Explanation
The graph of f(x) = 7^x has a horizontal asymptote at y = 0. Since g(x) = 7^x + 6 = f(x) + 6, every point on the graph shifts up 6 units, so its asymptote shifts from y = 0 to y = 6. Therefore, the true statement is that the asymptote of g(x) is the asymptote of f(x) shifted six units up.
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