I really dont understand how to describe polynomials from parent equations

Question

The question asks to describe the transformation from the parent equation y=x^3 and create transformed table. I do not fully understand how to make the table

Answer 1

Function transformations are applied generically to all functions in the following ways: 1) If a number is grouped with the x (as an addition or subtraction), it equates to a shift (translation) of the parent function in the x direction. 2) If a number is grouped with the y (as an addition or subtraction), it equates to a shift (translation) of the parent function in the y direction. 3) If the x is multiplied by a factor, it equates to a compression or stretch of the parent function in the x direction. 4) If the y is multiplied by a factor, it equates to a compression or stretch of the parent function in the y direction. 5) If the x is multiplied by a negative, it equates to reflecting the parent function across the y-axis, 6) If the y is multiplied by a negative, it equates to reflecting the parent function across the x-axis,

The devil is in the details however. The above is a simplified summary that has a lot of information and intricacies behind it. I'd be happy to meet with you to help explain it.