Option (C) F(x)= 3(x+2)^3 is the equation of this function after is reflected over the x-axis is the correct answer.
What is a reflection of transformation?
A reflection is a type of transformation. It maps one shape onto another. The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.
For the given situation,
The equation of this function [tex]f(x) = -3(x+2)^{3}[/tex]
The reflection of the function can be found by [tex]f(-x)[/tex]
⇒ [tex]f(-x)=-f(x)[/tex]
⇒ [tex]f(-x) =-( -3(x+2)^{3})[/tex]
⇒ [tex]f(x) = 3(x+2)^{3}[/tex]
Hence we can conclude that option (C) F(x)= 3(x+2)^3 is the equation of this function after is reflected over the x-axis is the correct answer.
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