Question

What are the vertical asymptote(s) and hole(s) for the graph of y =

Answer 1

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