Answer:
asymptotes: x= -4,-2 and no holes
Step-by-step explanation:
First we need to factor the denominator of the function
y = (x-1) / (x2 + 6x + 8)
x2 + 6x + 8 = 0
delta = b2 - 4ac = 36 - 32 = 4
x1 = (-6 + 2) / 2 = -2
x2 = (-6 - 2) / 2 = -4
So we have that x2 + 6x + 8 = (x+4)(x+2)
So our function is:
y = (x-1) / (x+4)(x+2)
As there is no common expressions in the numerator and denominator, there are no holes.
The asymptotes are when the denominator is zero, so:
(x+4)(x+2) = 0
x = -4 or x = -2
