Question

Write an equation of the translation of y=x^3 that has been moved 2 units up, 3 units to the right, and stretched by a factor of 4.

Answer 1

y=(4x-3)³+2

To shift the graph to the right 3 units, we subtract 3 before the exponent.  To shift it up 2 units, we add 2 to the end.  To stretch it by 4, we multiply x by 4 before the exponent.