Question

Determine the cubic function that is obtained from the parent function y = x^3

after each sequence of transformations

Vertical stretch by a factor of 3; vertical translation up 4 units; horizontal translation left 2 units

Answer 1

The answer here depends on whether you want to do them individually or collectively. If we go individually, then:

The vertical scaling gives us y = 3x³

The vertical translation gives us y = x³ + 4

The horizontal translation gives us y = (x + 2)³

On the other hand, if we want to apply all three at the same time, we get:

starting with a vertical scaling of 3, we get:

start with scaling: y = 3x³

add vertical translation: y = 3x³ + 4

and finally add horizontal translation: y = 3(x + 2)³ + 4