Final answer:
The end behavior of the function f(x)=-3(x+1)² (x-3) is that it approaches negative infinity as x approaches positive infinity and approaches positive infinity as x approaches negative infinity.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the leading term of the polynomial. In this case, the leading term is -3(x+1)² (x-3). The highest power of x in this polynomial is 2. When x approaches positive or negative infinity, the value of the expression -3(x+1)² (x-3) is determined by the sign of the leading term. Since the leading term has a coefficient of -3, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity and approaches positive infinity as x approaches negative infinity.