What Would be the translations of a y=x^3 function with the starting points, (1,1), (0,0), (1,1), and the endpoints (2, 0.5), (3,1), (4,1.5) and what would be the end equation

Answer 1

I suspect you meant (-1,-1), (0,0), (1,1) since those points fit y=x^3
That makes the horizontal shift +2, meaning the end equation ought to be
(x-2)^3 + k
Unfortunately, the vertical shifts are -0.5, 1.0, 0.5
so there is no single value of k which will work.

so, fix your problem, and you can probably work out the answer.