Apply the function transformation of g(x)=f(x-2)+4 to f(x)=x^3-8

Question

Describe the transformation and find the final form of the function after the transformation.

Answer 1

For f(x) equal to x³ − 8, f(x − 2) will give (x − 2)³ − 8.

Then g(x) = f(x − 2) + 4 will be written as (x − 2)³ − 8 + 4 or (x − 2)³ − 4 which expands and simplifies to

x³ − 6x² + 12x − 8 − 4 or x³ − 6x² + 12x − 12.

Transformation will draw an identical graph that is "picked up" and placed 4 units higher and 2 units farther to the right at all of its points.

Answer 2

For function transformations the number in the parenthesis with the x moves the function left or right, the number outside the parenthesis being added or subtracted at the end moves the function up or down.

(x-2) means move the function right 2, the + 4 means move up 4.

You need to apply these transformations to the original function.

Wherever there is an x replace it with x-2 and then add 4 at the end:

g(x) = f(x-2) + 4

= (x-2)^3 - 8 + 4

and simplify