Question

need help with this question please parts 2 and 3

Answer 1

Given:

$p(x)=3(x+3)^3+2$

(a) The parent function of p(x) is the cubic function:

$y=x^3$

(b) To produce p(x) from y, we need to perform the following transformations in order:

* Shift to the left 3 units. This gives the function:

$y=(x+3)^3$

* Stretch vertically by a factor of 3. This gives the function:

$y=3(x+3)^3$

* Shift upward 2 units. This gives the final function:

$p(x)=3(x+3)^3+2$

(c) The graphs of the parent function (in blue) and the transformed function (in red) are shown below: