Find all vertical and horizontal asymptotes of the graph of the given function. $f ( x ) = \frac { x ^ { 2 } - 3 x } { x ^ { 2 } + 5 x + 6 }$
A)Vertical asymptotes: x = -3,x = -2; horizontal asymptote: y = 1
B)Vertical asymptotes: x = -3,x = -2; horizontal asymptote: y = 3
C)Vertical asymptotes: x = -3,x = -2,x = 3; horizontal asymptote: y = 0
D)Vertical asymptotes: x = -3,x = -2,x = 3; horizontal asymptote: y = 1

Question

Quizplus · Accepted Answer

To find the vertical asymptotes, set the denominator equal to zero and solve for x: $x^2 + 5x + 6 = 0$ factors to $(x + 3)(x + 2) = 0$, giving $x = -3$ and $x = -2$. For the horizontal asymptote, since the degrees of the numerator and denominator are the same, divide the leading coefficients: $1/1 = 1$, so $y = 1$.

Find All Vertical and Horizontal Asymptotes of the Graph of the Given