Final answer:
The domain of the function is all real numbers except x = -2, and the range of the function approaches positive or negative infinity as x approaches positive or negative infinity, respectively.
Step-by-step explanation:
The domain and range of the function F(x) = (x^2 + 5x + 6)/(x + 2) can be determined by analyzing the restrictions on the function.
First, we need to find the values of x that make the denominator zero, since division by zero is undefined. So, setting x + 2 = 0, we find that x = -2.
Therefore, the domain of the function is all real numbers except x = -2. The range of the function can be determined by analyzing the behavior of the function as x approaches positive or negative infinity. Since the function is a rational function, the range will approach positive or negative infinity as x approaches positive or negative infinity, respectively.