Answer:
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
