Question

What is the vertical asymptote of the function f(x) = (x + 3) / (x² + 5x + 6)?

1) x = 3
2) x = 2
3) x = -2
4) x = -3

Answer 1

The vertical asymptotes of the function f(x) = (x + 3) / (x² + 5x + 6) are x = -3 and x = -2.

Step-by-step explanation:

The vertical asymptote of the function f(x) = (x + 3) / (x² + 5x + 6) can be found by determining the values of x that make the denominator (x² + 5x + 6) equal to zero.

To find these values, we can factor the denominator as (x + 3)(x + 2).

So, the vertical asymptotes occur when x + 3 = 0 or x + 2 = 0.

Solving these equations gives us x = -3 and x = -2. Therefore, the vertical asymptotes of the function f(x) = (x + 3) / (x² + 5x + 6) are x = -3 and x = -2.