Describe the end behavior of the graph of the polynomial function. \[ f(x)=2+3 x-4 x^{2}-5 x^{10} \] "Choose the correct answer below. B. $\uparrow$ c. $\sqrt{2}$ b.

Step 1 ：The end behavior of a polynomial function is determined by the degree and the leading coefficient of the polynomial. The degree of the polynomial is the highest power of x, and the leading coefficient is the coefficient of the term with the highest degree.

Step 2 ：In this case, the degree is 10 (from the term -5x^10) and the leading coefficient is -5.

Step 3 ：Since the degree is even and the leading coefficient is negative, the end behavior of the function is that as x approaches positive or negative infinity, f(x) approaches negative infinity.

Step 4 ：This means the graph of the function goes down or decreases without bound as we move to the right or left.

Step 5 ：So, the end behavior of the graph of the function is downwards.

Step 6 ：Final Answer: \(\boxed{B. \downarrow}\)