Final answer:
The end behavior of the function F(x) = -x^5 + 3x^4 -x^2 +5x -1 is that it increases without bound as x approaches negative infinity and decreases without bound as x approaches positive infinity.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the leading term, which is the term with the highest power of x. In the given function F(x) = -x^5 + 3x^4 -x^2 +5x -1, the leading term is -x^5.
When the leading term has an even exponent, like in this case, the function approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity.
Therefore, the end behavior of the function F(x) is that it increases without bound as x approaches negative infinity and decreases without bound as x approaches positive infinity.