C
1) In this question, we will identify the transformation by its algebraic representation and then match it with the corresponding graph.
2) Let's consider the parent function to be f(x)=x³-10 the transformed version is g(x) we can see that g(x) is:
• Horizontally translated
,
• Shifted Down.
So, we can write g(x) as:
![\begin{gathered} f(x)=x^(3)-10 \\ g(x)=(x-2)^3-10+16 \\ g(x)=(x-2)^3+6 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/kyyqf09c4nnsfp5s529jkxpm6clt739fod.png)
Thus, the answer is C