Cubic Function 949A86

1. **State the problem:** We are given the function $$h(x) = 3x^3 + 5$$ and we want to understand or analyze it. 2. **Formula and rules:** This is a cubic function of the form $$h(x) = ax^3 + b$$ where $$a = 3$$ and $$b = 5$$. 3. **Intermediate work:** The function is already simplified. It consists of a cubic term $$3x^3$$ and a constant term $$5$$. 4. **Explanation:** - The cubic term $$3x^3$$ dominates the behavior of the function for large values of $$x$$. - The constant $$5$$ shifts the graph vertically upwards by 5 units. - The function is continuous and differentiable everywhere. 5. **Summary:** The function $$h(x) = 3x^3 + 5$$ is a cubic polynomial with a vertical shift of 5. No further simplification is needed.