Given:
[tex]p(x)=3(x+3)^3+2[/tex]
(a) The parent function of p(x) is the cubic function:
[tex]y=x^3[/tex]
(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:
[tex]y=(x+3)^3[/tex]
* Stretch vertically by a factor of 3. This gives the function:
[tex]y=3(x+3)^3[/tex]
* Shift upward 2 units. This gives the final function:
[tex]p(x)=3(x+3)^3+2[/tex]
(c) The graphs of the parent function (in blue) and the transformed function (in red) are shown below:
