Polynomial Check E77558
1. The problem asks to identify which given functions are polynomial functions.
2. A polynomial function is defined as a function of the form $$p(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$$ where the exponents are non-negative integers and coefficients are real numbers.
3. Let's analyze each function:
- I: $$p(x) = \frac{1}{2} x^3 - 3x^2 + 1$$
This is a polynomial because all exponents are non-negative integers (3, 2, 0) and coefficients are real numbers.
- II: $$p(x) = \frac{1}{x^3} + \frac{2}{x^2} + 3/x = x^{-3} + 2x^{-2} + 3x^{-1}$$
This is not a polynomial because it contains negative exponents.
- III: $$p(x) = \sqrt{2x^3 - 3x^2 + 2x - 1}$$
This is not a polynomial because of the square root, which is not allowed in polynomial functions.
4. Therefore, only function I is a polynomial function.
Final answer: Pernyataan yang sesuai adalah I saja.