Math  /  Algebra

Question27) Find the function of g(x)g(x) by using function f(x)f(x). A) g(x)=f(x3)+2g(x)=-f(x-3)+2 B) g(x)=f(x+3)+6g(x)=-f(x+3)+6 C) g(x)=f(3x)+2g(x)=-f(3-x)+2 D) g(x)=f(x3)+6g(x)=-f(x-3)+6

Studdy Solution
Combine the transformations: a horizontal shift of 3 units to the right, a reflection over the x-axis, and a vertical shift.
The reflection over the x-axis suggests multiplying by 1-1, and the vertical shift is adjusted to match the options.
The correct transformation is:
g(x)=f(x3)+6 g(x) = -f(x-3) + 6
This corresponds to option D.
D)g(x)=f(x3)+6 \boxed{D) \, g(x) = -f(x-3) + 6}

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