Answer:
[tex]g(x)=(x-3)^{3}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we have
[tex]f(x)=x^{3}[/tex]
The inflexion point of the function f(x) is the point [tex](0,0)[/tex] (origin)
The figure shown in the graph has the inflexion point at point [tex](3,0)[/tex]
therefore
the rule of the translation of f(x) to g(x) is equal to
[tex](x,y)------> (x+3,y)[/tex]
That means-----> The translation is [tex]3[/tex] units to the right
so
The equation of the function g(x) is
[tex]g(x)=(x-3)^{3}[/tex]
