Question

The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form
g(x) = (x – h)3 + k.

Answer 1

Answer:

g(x) = (x-4)³ - 2 ,  h = 2, k=2.

Step-by-step explanation:

Given : The parent function f(x) = x3 is translated to form g(x),

To find : The translated function can be written in the form

g(x) = (x – h)³ + k.

Solution : We have given  parent function f(x) = x³

We can see from the graph , graph is shifted down by 2 units and shifted to right by 4 units .

By the transformation rule : f(x) →→f(x -h) graph would shift to right by h units and f(x) - k mean graph would shift down by k units.

Here, h =  4 and k = 2

g(x) = (x-4)³ - 2.

Therefore, g(x) = (x-4)³ - 2 ,  h = 2, k=2.

Answer 2

Answer:

First option

h = 4 and k = - 2

Step-by-step explanation:

f(x) = x^3 translated to g(x) = (x – h)^3 + k.

f(x) transformed to g(x) with 4 units to the right and 2 units down

g(x) = (x - 4)^3 - 2

h = 4 and k = - 2