Determine the vertical asymptotes and holes for the graph of the equation below. y=(x+7)/(x^2+8x+7) Please show all steps to solve!

Question

Determine the vertical asymptotes and holes for the graph of the equation below.

y=
`(x+7)/(x^2+8x+7)`

Please show all steps to solve!

Answer 1

Since x ² + 8x + 7 = (x + 7) (x + 1), we have for x ≠ -7,

y = (x + 7) / (x ² + 8x + 7) = 1/(x + 1)

so y is undefined at x = -1, indicating a vertical asymptote, and there is a hole/removable discontinuity at x = -7. Then the answer is D.