Questions: 3x = -(π/2)x - 4n - 37^7(x + n)

Solution Steps

The given polynomial function is $g(x) = -\frac{1}{2}x^4 + 4x^3 - 9x^2 + x + 10$. The leading term is $-\frac{1}{2}x^4$. Since the degree is even (4) and the leading coefficient is negative ($-\frac{1}{2}$), the end behavior of the graph is that it falls to the left and falls to the right.

Among the given graphs, only options A and C have the end behavior where the graph falls to both the left and the right.

Since we don't have enough information to find precise roots and turning points, we can use the y-intercept. The y-intercept is the value of the function at x=0, which is g(0) = 10. Option A has a y-intercept at approximately 10 while Option C has a y-intercept at approximately -10.

Final Answer: The correct answer is A.