Question

Describe the vertical asymptote(s) and hole(s) for the graph of y = x minus five over x squared plus four x plus three.
A. asymptotes: x = –3, –1 and no holes.
B. asymptote: x = –3 and hole: x = –5
C. asymptotes: x = –3, –1 and hole: x = –5
D. asymptote: x = –5 and hole: x = –3

Answer 1

geez - learn how to type math, okay?
AAAaannndd the bot gets it wrong yet again!

y = (x-5)/(x^2+4x+3)
y = (x-5) / (x+1)(x+3)
so A
The x-5 numerator means there is a zero at x-5, not a hole.
And there is a horizontal asymptote at y=0

Answer 2

C. asymptotes: x = –3, –1 and hole: x = –5

Answer 3

because as x approaches positive or negative infinity, the denominator (x^2+4x+3) grows much faster than the numerator (x-5), causing the fraction to approach 0.