Identify the vertical asymptotes of f(x) = quantity x minus 4 over quantity x squared plus 13 x plus 36

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.

x = -9 and x = -4 are the two asymptotes.

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)

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