F(x)=1/3x^3+5x^2; f(x)=2x^3-3x^2-2; f(x)=2x^4-3x^2+5

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It seems like you have written three different functions here. Let's break them down one by one:

F(x) = (1/3)x^3 + 5x^2
This function is a polynomial of degree 3. The leading term is (1/3)x^3 and the constant term is 0. The graph of this function would be a curve that opens upwards.

f(x) = 2x^3 - 3x^2 - 2
This function is also a polynomial of degree 3. The leading term is 2x^3 and the constant term is -2. The graph of this function would be a curve that opens upwards as well.

f(x) = 2x^4 - 3x^2 + 5
This function is a polynomial of degree 4. The leading term is 2x^4 and the constant term is 5. The graph of this function would be a curve that might have multiple turning points depending on the coefficients of the terms.

If you have any specific questions or need further clarification, feel free to ask.