Final answer:
Shifting the function F(x) = x³ up 3 units and flipping it across the x-axis, under an assumption of a typo, results in the function F(x) = -x³ + 3, which is not explicitly listed among the given options.
Step-by-step explanation:
If you shift the cubic parent function, F(x) = x³, up 3 units and then flip it across the x-axis, you would first translate the graph upwards, which results in the function F(x) = x³ + 3. Flipping it across the x-axis is equivalent to multiplying the entire function by -1, making the function F(x) = -(x³ + 3). However, we must distribute the negative sign properly, yielding F(x) = -x³ - 3. This matches none of the given options directly. However, if we're assuming a typographical error and that 'up 3 units' should result in a vertical shift reflected in the constant term, and not in the cube term, then the correct option would be F(x) = -x³ + 3.