The graph of f(x) can be compressed vertically and shifted to the left to
produce the graph of g(x). if f(x) = x3, which of the following could be the
equation of g(x)?

G(x) = 1/3 (x + 2)³  ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve the problem

- If the function f(x) translated horizontally to the left  by h units, then

 the new function g(x) = f(x + h)

- If the function f(x) compressed vertically, then g(x) = k · f(x), where

 0 < k < 1 (multiplying each of its y-coordinates by k)

* Lets solve the problem

∵ F(x) = x³

∵ F(x) is compressed vertically

∴ F(x) multiplied by a fraction between 0 and 1

∴ G(x) = k (x³)

∵ F(x) is shifted horizontally to the left

∴ The x add by the shifted units

∴ G(x) = k (x + h)³

* Lets look to the answer to find G(x)

∵ G(x) = 1/3 (x + 2)³  

∴ K = 1/3 ⇒ 0 < 1/3 < 1

∴ h = 2 ⇒ + for left shifted

∴ G(x) = 1/3 (x + 2)³  

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