Question

How does the graph of g(x) = (x - 3)^3 + 4 compare to the parent function f(x) = x^3?

Answer 1

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.

Explanation:

we know that

`f(x)=x^(3)` ----> the turning point is the point (0,0)

`g(x)=(x-3)^(3)+4` ----> the turning point is the point (3,4)

The rule of the translation of f(x) to g(x) is equal to

(x,y) ------> (x+3,y+4)

That means-----> The translation is 3 units at right and 4 units up

therefore

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.