• The addition of a number from the x-term ,within, the radical shifts to right/left (depending on the sign of the addend.
,
• The addition/subtraction ,outside the radical ,shifts down/up the function
1) The best way to tackle this question is to think of the simplest function of this family, in this case, let's consider the function:
![y=\sqrt[3]{27x}](https://img.qammunity.org/2023/formulas/mathematics/college/a8ysahhvd597xlcvnt7vi4lzebzdbv79f1.png)
2) Note that now we can compare this function to that one that we were given.
![y=\sqrt[3]{27x-81}-5](https://img.qammunity.org/2023/formulas/mathematics/college/yai0yg5gqe0ohasm5v4gybtadx6w1i6wbr.png)
Note that, inside the root, in the radicand, we can see a -81. The addition/subtraction of a number inside the radical moves to the right or to the left. In this case, this moves the function to the Right. As we can see:
We can also see that the second function has been shifted down to 5 units (notice the number outside the parentheses shifting the function down).
3) So the answer is:
• The addition of a number from the x-term ,within, the radical shifts to right/letft (depending on the sign of the addend.
,
• The addition/subtraction ,outside the radical ,shifts down/up the function