Question

How does the graph of g(x) = (x − 3)3 + 4 compare to the parent function f(x) = x3?

g(x) is shifted 3 units to the right and 4 units up.
g(x) is shifted 4 units to the right and 3 units up.
g(x) is shifted 3 units to the left and 4 units up.
g(x) is shifted 4 units to the right and 3 units down.

Answer 1

Option a is right.

Explanation:

Given that the parent function is the cubic funciton

`f(x) = x^3`

This is transformed to get a new function

as
`(x-3)^3+4 =g(x)`

The new function is obtained 4 units up i.e. vertical shift of 4 units and horizontal shift of 3 units to the right.

g(x) is shifted 3 units to the right and 4 units up

Option a is right

Answer 2

g(x) is shifted 3 right and 4 up

Explanation:

y=a(x-h)^3 +k

h=3

k=4

(3,4) is the center of the equation. This is (0,0) for the parent function y=x^3.

3 is 3 units to the right of 0, and y is 4 units up from 0. Therefore, the equation is shifted 3 to the right and 4 up.