Question

Identify the vertical asymptotes of f(x)= x-4 over x2+13x+36

A) x= -9 and x= -4
B) x= -9 and x=4
C) x=9 and x=-4
D) x=9 and x=4

Answer 1

Given:
f(x) = (x-4)/(x² + 13x + 36)

The vertical asymptotes of f(x) occur when the denominator is zero because f(x) becomes undefined.

Note that
x² + 13x + 36 = (x + 4)(x + 9).
Therefore
f(x) = (x - 4)/[(x + 4)(x + 9)]

The denominator is zero, when
(a) x + 4 = 0 => x = -4, or
(b) x + 9 = 0 => x = -9.

Therefore the function becomes undefined a x = -4, or x = -9, where the vertical asymptotes occur.

Answer: A) x = -9 and x = -4.