Describe how the cubic functions g(x) and h(x) have been transformed from the parent function f(x).
f(x) = x^3
g(x) = -(x - 5)^3
h(x) = 5x^3 - 2
The cubic function g(x) has been shifted 5 units to the right compared to the parent function f(x). This can be seen in the equation where (x - 5) is inside the parentheses, indicating the horizontal translation.
The cubic function h(x) has been stretched vertically by a factor of 5 compared to the parent function f(x). This can be seen in the equation where 5 is multiplied by x^3, indicating the vertical dilation.
Additionally, the cubic function h(x) has been shifted 2 units downward compared to the parent function f(x). This can be seen in the equation where -2 is subtracted, indicating the vertical translation.