Answer:
- hole: x = -4
- vertical asymptote: x = 1
- horizontal asymptote: y = -1
Explanation:
The function factors as ...
... f(x) = -(x+3)(x+4)/((x-1)(x+4)) = -(x+3)/(x-1) . . . . x ≠ -4
and the quotient is ...
... f(x) = -(1 +4/(x-1))
... f(x) = -1 -4/(x-1) . . . . . x ≠ -4
This has a hole at x = -4 (where the denominator factor cancels the numerator factor), a vertical asymptote at x=1 (where the denominator is zero), and a horizontal asymptote at y = -1 (the value of the function for large values of x).