Question

Rewrite (see image) to make it easy to graph using a translation, Describe the graph.I need help understanding the step by step steps to solve this problem.

Answer 1

• 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:

$y=\sqrt[3]{27x}$

2) Note that now we can compare this function to that one that we were given.

$y=\sqrt[3]{27x-81}-5$

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