Final answer:
The end behavior of the function f(x) results from the highest power term, which is 6x^5. As x approaches infinity, f(x) goes to infinity, and as x approaches negative infinity, f(x) goes to negative infinity.
Step-by-step explanation:
The question asks about the end behavior of the polynomial function f(x) = 1152x^3 + 6x^5 + 138x^4 - 7776 + 2592x + 3888x^2.
To determine this, we look at the term with the highest power of x, which in this case is 6x^5. This term will dominate the others as x becomes very large or very small.
Because the coefficient of the highest power is positive, as x approaches infinity, f(x) will also approach infinity. Similarly, as x approaches negative infinity, since the highest power is odd, f(x) will approach negative infinity.
Thus, we can conclude that the end behavior of the polynomial is such that as x goes to infinity, f(x) goes to infinity, and as x goes to negative infinity, f(x) goes to negative infinity.