Answer:
[tex]g(x)=(x+2)^{3}-4[/tex]
Step-by-step explanation:
we know that
The parent function is
[tex]f(x)=x^{3}[/tex]
The turning point in the parent function is the origin (0,0)
In the translated function g(x) the turning point is (-2,-4)
so
The rule of the translation of f(x) to g(x)
(0,0) -----> (-2,-4)
(x,y) ----> (x-2,y-4)
That means ---> The translation is 2 units at left and 4 units down
therefore
The equation of the translated function is
[tex]g(x)=(x+2)^{3}-4[/tex]
