Final answer:
The polynomial function that imitates the given end behavior is (c) (4x^4 - 2x^3 + x^2 + 3x - 6).
Step-by-step explanation:
Based on the given information, we are looking for a polynomial function that has a positive value and a decreasing positive slope as x increases. The option that could correspond to f(x) is (c) (4x^4 - 2x^3 + x^2 + 3x - 6).
When x = 3, the value of f(x) will be positive because all the terms have positive coefficients. The decreasing positive slope can be observed by analyzing the coefficients of the polynomial. The power of x decreases with each term, indicating a decreasing slope. Therefore, option (c) imitates the end behavior described in the question.