Question

If the parent function is f(x) = x3, which transformed function is shown in the graph? g(x) = (x − 3)3 , g(x) = (x + 3)3 , g(x) = x3 + 3 , g(x) = x3 − 3

Answer 1

`g(x)=(x-3)^(3)`

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)`