Final answer:
To find the range of F(x) = -x - 2 with the domain x > 3, we determine that as x increases, F(x) decreases without bound, resulting in a range of y | y < -5.
Step-by-step explanation:
The student has asked about finding the range of the function F(x) = -x - 2 with a given domain of x > 3. Since the domain restricts x to values greater than 3, we must find how this affects the range of F(x). The function F(x) is linear, and as x increases, F(x) decreases because of the negative coefficient in front of x. Since the lowest value x can take is just greater than 3 (approaching 3 but not including it), we can substitute this into the function to find the highest value F(x) can take, which is just less than F(3) = -5.
Because the function continues to decrease without bound as x increases, there is no lower limit to the range. Thus, the range of F(x) is y | y < -5.