Answer :
Final answer:
The end behavior of the polynomial function with the highest power of 6 and a positive leading coefficient is that the function approaches infinity as x approaches both positive and negative infinity.
Explanation:
The end behavior of the function f(x) = 1536x + 30x4 + 7680 - 60x5 + 1440x3 - 4800x2 + 6x6 is determined by the highest power term. Since the highest power of x is 6 and the coefficient is positive (6), as x approaches infinity, f(x) will also approach infinity, and as x approaches negative infinity, f(x) will approach positive infinity due to the even power of x. This function is a polynomial of degree 6, which generally has an end behavior resembling that of an even function, where both ends of the function extend upwards.
