Apply the function transformation of g(x) = f(x - 2) + 4 to f(x) = x3 - 8. Describe the transformations and find the final form of the function after the transf

Question

Apply the function transformation of g(x) = f(x - 2) + 4 to f(x) = x^3 - 8. Describe the transformations and find the final form of the function after the transformation.

Please help me with this question, I don't understand it. Thank you

Answer 1

The new function is obtained by shifting right 2 units and up four units.

Specifically,

 

(x-2)^3 - 8 + 4 =  

 

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

 

x^3 - 4x^2 + 4x 

       - 2x^2 +8x - 8 - 8 + 4 =

 

x^3 - 6x^2 + 12x - 12