Which statement about f of x and its translation, g of x , is true? f of x is equal to 2 fifths to the x th power g(x)=((2)/(5))^x−3
Answer
A
The range of g of x is, start set y such that y is greater than 0 end set and the range of f of x is start set y such that y is greater than negative 3 end set .
B
The asymptote of g of x is the asymptote of f of x shifted three units up.
C
The asymptote of g of x is the asymptote of f of x shifted three units down.
D
The range of g of x is, start set y such that y is greater than 3 end set and the range of f of x is start set y such that y is greater than 0 end set .
Explanation
The graph of f(x) = (2/5)^x has horizontal asymptote y = 0. Subtracting 3 to get g(x) = (2/5)^x − 3 shifts the graph, including its asymptote, three units down to y = −3. Therefore, the true statement is that the asymptote of g(x) is the asymptote of f(x) shifted three units down.
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