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