The given polynomial is g(n) = 71n^12 - 11n^4 - 5n - 20. To determine the end behavior of the polynomial, we need to analyze the coefficients of the polynomial and the powers of the variable n.
From the given polynomial, we can see that the coefficient of n^12 is 71, which is a positive integer. This means that as n increases, the value of the polynomial will increase. Additionally, the coefficient of n^4 is -11, which is a negative integer. This means that as n increases, the value of the polynomial will decrease. The coefficient of n is -5, which is a negative integer, and the constant term is -20, which is a negative integer.
Based on these observations, we can conclude that the end behavior of the polynomial is downward. As n increases, the value of the polynomial will first increase, then decrease, and finally approach negative infinity as n becomes very large.
Therefore, the correct answer is (d) Down —> Down.