Step 1 :The problem is asking for a polynomial function that might have the given graph. The graph is not provided here, but we know that the point (-2,18) lies on the graph. We can use this information to test each of the given polynomial functions. If the function evaluates to 18 when x is -2, then it could be the function for the graph.
Step 2 :Test each function by substituting x=-2 into each function.
Step 3 :The function that evaluates to 18 when x is -2 is B. Therefore, the polynomial function that might have the given graph is B.
Step 4 :Final Answer: \(\boxed{B. f(x)=\frac{1}{2}(x+1)(x-1)^{2}(x-2)}\)