To determine the cubic function that is obtained from the parent function, consider the transformations one at a time.
y=6(x+3)^3
Practice makes perfect
To determine the cubic function that is obtained from the parent function y=x^3 after the given sequence of transformations, let's consider the transformations one at a time.
Vertical Stretch by a Factor of 6
We will start by performing a vertical stretch on the parent function by a factor of 6. This is done by multiplying the parent function by 6. The resulting function is y=6x^3.
Horizontal Translation 3 Units Left
Finally, to perform a horizontal translation 3 units left, we need to add 3 to the x-variable, resulting in y=6(x+3)^3.
The cubic function that is obtained after the sequence of transformations is y=6(x+3)^3.
