Given a parent function y=x^3, write a function with the following transformations: right 3, up 2, dilated by a factor of 1/2.

h(x) = (1/2)(x - 3)^2 + 2

Step-by-step explanation:

Start with y = x^3.

Multiply x^3 by the dilation factor (1/2); this compresses the graph vertically.

Next, replace the x in x^3 with (x - 3).  This shifts the graph 3 units to the right.

Last, starting with your g(x) = (1/2)(x - 3)^2, add 2

You will end up with h(x) = (1/2)(x - 3)^2 + 2.