Find all vertical and horizontal asymptotes of the graph of the given function. $$f ( x ) = \frac { x ^ { 2 } - 2 x } { x ^ { 2 } - 8 x + 15 }$$
A) Vertical asymptotes: x = 5, x = 3, x = 2; horizontal asymptote: y = 0
B) Vertical asymptotes: x = 5, x = 3, x = 2; horizontal asymptote: y = 1
C) Vertical asymptotes: x = 5, x = 3; horizontal asymptote: y = 2
D) Vertical asymptotes: x = 5, 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: $x^2 - 8x + 15 = 0$ factors to $(x - 5)(x - 3) = 0$, so the vertical asymptotes are at $x = 5$ and $x = 3$. For the horizontal asymptote, since the degrees of the numerator and denominator are the same, divide the leading coefficients: $1/1 = 1$, so the horizontal asymptote is $y = 1$.

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