## Calculus: Early Transcendentals 8th Edition

vertical asymptotes: $x=1$ $x=-1$ $x=0$ horizontal asymptote: $y=-1$
To first find out vertical asymptotes, we can take the denominator of the function and factor it out into $(x+x^{2})(x-x^{2})$. By solving for when y=0, we come up with vertical asymptotes of x=1, x=−1, x=0. To find our horizontal asymptotes, we can take the coefficients of the highest degree in each polynomial. Because both of these are of the second degree, we can divide them to yield $\frac{x^{4}}{-x^{4}}$ to get an asymptote at y=-1