Expression: f(x) = [x - 4] / [x^2 + 13x + 36].
The vertical asympotes is f(a) when the denominator of f(x) is zero and at least one side limit when you approach to a is infinite or negative infinite.
The we have to factor the polynomial in the denominator to identify the roots and the limit of the function when x approachs to the roots.
x^2 + 13x + 36 = (x + 9)(x +4) => roots are x = -9 and x = -4
Now you can write the expresion as: f(x) = [x - 4] / [ (x +4)(x+9) ]
Find the limits when x approachs to each root.
Limit of f(x) when x approachs to - 4 by the right is negative infinite and limit when x approach - 4 by the left is infinite, then x = - 4 is a vertical asymptote.
Limit of f(x) when x approachs to - 9 by the left is negative infinite and limit when x approach - 9 by the right is infinite, then x = - 9 is a vertical asymptote.
Answer: x = -9 and x = -4 are the two asymptotes.
