Question

Part A

A function f(x)=x3 is transformed into the function g(x)=2x−43+5. Name and explain in complete sentences the transformations that occurred to the parent cube root function.

Part B
How is the general shape of a cube root function different from the shape of a square root function?

Answer 1

The graph of g(x) will be shifted 4 units up and 1 unit to the right

Explanation:

The parent function f(x) = x^3 is transformed to g(x) = (x – 1)^3 + 4

Parent function f(x)= x^3

If any number is added at the end then the graph will be shifted up

If any number is subtracted from x then graph will be shifted right

f(x)----> f(x) + a (shifted 'a' units up)

f(x) ----> f(x-a) (shifted 'a' units right)

g(x) = (x – 1)^3 + 4

The graph of g(x) will be shifted 4 units up and 1 unit to the right

the graph is attached below