Precalculus help

Question

Consider the graph of y=x^3. It is slid 3 units to the left, then reflected in the x-axis, and finally slid 8 units down. What is the resulting equation?

Answer 1

A general "form", if you will, to represent transformations of the cubic function is y = a(x - h)^3 + k, where

1. a could indicate a vertical stretch, shrink, or reflection
2. h would indicate a horizontal translation
3. k would indicate a vertical translation

Doing your 3 transformations in order, a horizontal translation to the left 3 units (so h = -3), would be y=(x+3)^3. If we reflect this over the x-axis, we now have y=-(x+3)^3. Lastly, if you translate this function 8 units down, k = -8... so y = - (x+3)^3 - 8