Answer: Option b.
Step-by-step explanation:
1. You have the following parent function given in the problem above:
f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)
2. If you take the parent function and make y=f(x+3), then you have:
[tex]y=f(x+3)=(x+3)^{3}[/tex] (The function is shifted 3 units left on the x-axis).
3. Then you if you make y=f(x+3)-2, as following, you obtain:
[tex]y=f(x+3)-2=(x+3)^{3}-2[/tex] (The function is shifted 2 units down on the y-axis).
4. Therefore, that is how you obtain the final function.
The answer is the graph shown in the option b.
