Answer: Choice C
The vertical asymptote at x = -4 tells us that -4 is not part of the domain. This only applies to 1/(x+4). If we plug in x = -4, we get...
f(x) = 1/(x+4)
f(-4) = 1/(-4+4)
f(-4) = 1/0
f(-4) = undefined; because of the division by zero error
The value x = -4 is allowed in the other answer choices.